Abstract Concepts & Conversation: Analysis, Experiment 2
Bodo Winter
2/6/2021
1 Introduction
This script is structured as follows:
- setup: loading packages and data
- overview: displaying values such as N of participants, items, etc.
- preprocessing: data wrangling steps
- descriptive statistics: summary stats for said patterns
- data visualization: visualizing the main data patterns we want to report
- data visualization: covariates: plots for each covariate in relationship with IOS
Main bits necessary to understand the following analysis:
- the column
categorydifferentiatesabstractversusconcrete - the column
subclusterdifferentiates different types of abstract and concrete concepts - the two main dependent variables are
closenessandIOS(self-other inclusion)
The following baseline analyses will be performed:
- assess correlations between covariates
- assess the effect of all covariates on
IOS - assess the effect of all covariates on
closeness
The following main analyses will be performed:
- assess the interaction of
categoryandother_inclusiononIOS - assess the interaction of
categoryandother_inclusiononcloseness - assess the interaction of
categoryandself_inclusiononIOS - assess the interaction of
categoryandself_inclusiononcloseness - repeat all those models for
subclusterto zoom into the more detailed category structure of abstract concepts
We will look additionally also at difficulty:
- assess the effect of
categoryondifficulty, and in a separate model ofsubcluster - perform both main analyses again, this time controlling for
difficulty
For all brms model fits, corresponding code chunks are
set to eval = FALSE in the final file with pre-compiled
models saved in models folder that are loaded into this
script to save the user time.
2 Setup
Load packages:
library(tidyverse) # for data processing
library(brms) # for Bayesian mixed models
library(tidybayes) # for half-eye plots of posteriors
library(ggridges) # for joy plots
library(patchwork) # for multiplot arrays
library(gridExtra) # for multiplot arrays when patchwork fails us
library(plotly) # for scatterplot matrix
library(GGally) # for scatterplot matrixLoad data:
# Load data:
df <- read_csv('../data/abstract_concepts_conversations_all_E2.csv')
# Show some random rows:
sample_n(df, 5)## # A tibble: 5 × 13
## participant word category subcluster passive_closeness active_closeness
## <dbl> <chr> <chr> <chr> <dbl> <dbl>
## 1 136 Cactus Concrete Conc_an 83 81.1
## 2 115 Cactus Concrete Conc_an 79.6 77.6
## 3 26 Zucca Concrete Conc_an 88.9 90.2
## 4 94 Abitudine Abstract SS 43.4 48.1
## 5 57 Giuramento Abstract EM 96.4 96
## # ℹ 7 more variables: pleasantness <dbl>, commitment <dbl>, intimacy <dbl>,
## # difficulty <dbl>, self_contribution <dbl>, other_contribution <dbl>,
## # IOS <dbl>3 Data cleaning and processing
For the main model later, we want to look at how category influences
IOS when interacting with other_contribution. For this we
need to center other_contribution first. We’ll do this here
already so that subsets of this data also contain the centered covariate
other_contribution_c. We’ll later also use
difficulty as a control covariate, so let’s center that as
well just in case.
df <- mutate(df,
other_contribution_c = other_contribution - mean(other_contribution,
na.rm = TRUE),
self_contribution_c = self_contribution - mean(self_contribution,
na.rm = TRUE),
difficulty_c = difficulty - mean(difficulty,
na.rm = TRUE))Also change the content of the category column so that
the labels say abstract and concrete, and make
the latter come first, which is more intuitive:
df <- mutate(df,
category = str_to_lower(category),
category = factor(category,
levels = c('concrete', 'abstract')))Check the content of the subcluster column, which
contains more detailed breakdowns of different kinds of concepts.
df %>%
count(subcluster)## # A tibble: 6 × 2
## subcluster n
## <chr> <int>
## 1 Conc_an 278
## 2 Conc_in 266
## 3 EM 174
## 4 PS 136
## 5 PSTQ 136
## 6 SS 98# Compare:
df %>%
count(category)## # A tibble: 2 × 2
## category n
## <fct> <int>
## 1 concrete 544
## 2 abstract 544Slightly uneven distribution for the different subclusters, with
relatively fewer SS concepts (= self-sociality), and
slightly more EM concepts (= emotional).
Let’s give them more transparent labels, which is also useful for
plotting later. We’ll call the new column spellout, because
it “spells out” the abbreviations.
df <- mutate(df,
spellout = case_when(
subcluster == 'Conc_an'~ 'concrete animate or organic',
subcluster == 'Conc_in'~ 'concrete inanimate or inorganic',
subcluster == 'EM'~ 'abstract emotional',
subcluster == 'PSTQ'~ 'abstract quantitative-temporal-spatial',
subcluster == 'PS'~ 'abstract philosophical-spiritual',
subcluster == 'SS'~ 'abstract self-sociality'
))Check the correlation between active and passive closeness:
with(df, cor.test(active_closeness, passive_closeness))##
## Pearson's product-moment correlation
##
## data: active_closeness and passive_closeness
## t = 89.297, df = 1086, p-value < 2.2e-16
## alternative hypothesis: true correlation is not equal to 0
## 95 percent confidence interval:
## 0.9306087 0.9449012
## sample estimates:
## cor
## 0.9381534r = 0.94, very highly correlated. Let’s average them for the main
analysis. The new variable will be called closeness, and
the average of active_closeness and
passive_closeness.
df <- mutate(df,
closeness = (active_closeness + passive_closeness) / 2)The closeness dependent measure is a VAS scale between 0
and 100. This needs to be scaled to [0, 1] for the beta distribution. We
will call the new variable that is scaled this way
closeness_01.
df <- mutate(df, closeness_01 = closeness / 100)4 Overview, preprocessing, and exclusions
Check participants prior to exclusion:
# Count rows per participants:
df %>%
count(participant)## # A tibble: 136 × 2
## participant n
## <dbl> <int>
## 1 1 8
## 2 2 8
## 3 3 8
## 4 4 8
## 5 5 8
## 6 6 8
## 7 7 8
## 8 8 8
## 9 9 8
## 10 10 8
## # ℹ 126 more rows# Count rows of this table to print number of participants into console:
df %>%
count(participant) %>%
nrow()## [1] 136136 participants.
Let’s exclude the participants that are meant to be excluded. This information comes directly from Chiara, and specifically, I am supposed to exclude participants 72, 8, 74, 129, 111, 55, and 53. We’ve checked these and they do indeed look odd, seemingly responding like straightliners.
# Define exclusion vector:
bad_ones <- c(72, 8, 74, 129, 111, 55, 53)
# Exclude:
df <- filter(df,
!(participant %in% bad_ones))
# Check:
df %>%
count(participant) %>%
nrow()## [1] 129Seven participants less, which is correct.
Now let’s do the same for words (= items):
# Count rows per participants:
df %>%
count(word)## # A tibble: 32 × 2
## word n
## <chr> <int>
## 1 Abitudine 31
## 2 Aereo 31
## 3 Attenzione 30
## 4 Bottiglia 31
## 5 Brivido 35
## 6 Cactus 30
## 7 Causa 31
## 8 Enigma 33
## 9 Fama 35
## 10 Favola 35
## # ℹ 22 more rows# Count rows of this table to print number of participants into console:
df %>%
count(word) %>%
nrow()## [1] 3232 items.
What are these words?
distinct(df, subcluster, word) %>%
sample_n(20)## # A tibble: 20 × 2
## subcluster word
## <chr> <chr>
## 1 PS Tendenza
## 2 Conc_an Cactus
## 3 Conc_in Tavolo
## 4 EM Favola
## 5 Conc_an Gallo
## 6 EM Giuramento
## 7 Conc_in Aereo
## 8 PS Causa
## 9 Conc_in Quaderno
## 10 PSTQ Brivido
## 11 Conc_an Pescatore
## 12 Conc_an Turista
## 13 PS Enigma
## 14 Conc_an Insalata
## 15 EM Scherzo
## 16 Conc_in Pentola
## 17 Conc_an Zucca
## 18 PSTQ Inizio
## 19 Conc_an Sarto
## 20 SS AttenzioneFor presentation purposes only, dichotomize the
other_contribution variable, and order it in such a way
that low other comes before high other. This
will be used in the median_split_p code chunk below as
well.
# Calculate median:
md <- median(df$other_contribution)
# Create median split variable:
df <- mutate(df,
other_cat = ifelse(other_contribution > md,
'high other contribution',
'low other contribution'),
other_cat = factor(other_cat,
levels = c('low other contribution',
'high other contribution')))Let’s look at the average IOS for abstract and concrete as a function of the median split:
df %>%
group_by(other_cat, category) %>%
summarize(M_IOS = mean(IOS),
M_dist = mean(closeness))## `summarise()` has grouped output by 'other_cat'. You can override using the
## `.groups` argument.## # A tibble: 4 × 4
## # Groups: other_cat [2]
## other_cat category M_IOS M_dist
## <fct> <fct> <dbl> <dbl>
## 1 low other contribution concrete 3.03 65.8
## 2 low other contribution abstract 2.91 66.0
## 3 high other contribution concrete 3.52 73.5
## 4 high other contribution abstract 3.66 74.5Although it only comes up later, we’ll set the reference levels for
subcluster here now:
df <- mutate(df,
subcluster = factor(subcluster),
subcluster = relevel(subcluster, ref = 'PSTQ'))
# Check:
levels(df$subcluster)## [1] "PSTQ" "Conc_an" "Conc_in" "EM" "PS" "SS"5 Descriptive statistics
Calculate closeness as a function of
category and subcluster:
# Category (abstract versus concrete):
df %>%
group_by(category) %>%
summarize(M = mean(closeness))## # A tibble: 2 × 2
## category M
## <fct> <dbl>
## 1 concrete 69.8
## 2 abstract 70.1# Subcluster:
df %>%
group_by(spellout) %>%
summarize(M = mean(closeness)) %>%
arrange(desc(M))## # A tibble: 6 × 2
## spellout M
## <chr> <dbl>
## 1 abstract quantitative-temporal-spatial 70.7
## 2 abstract emotional 70.5
## 3 concrete animate or organic 70.3
## 4 abstract philosophical-spiritual 69.5
## 5 abstract self-sociality 69.4
## 6 concrete inanimate or inorganic 69.2Check self_contribution and
other_contribution for the different subclusters. Chiara
says that self-sociality and emotional abstract concepts should be more
interacting with self-contribution, and philosophical more with
other-contribution.
# Self contribution:
df %>%
group_by(spellout) %>%
summarize(self = mean(self_contribution)) %>%
arrange(desc(self))## # A tibble: 6 × 2
## spellout self
## <chr> <dbl>
## 1 concrete inanimate or inorganic 71.3
## 2 abstract self-sociality 71.0
## 3 abstract philosophical-spiritual 70.7
## 4 abstract quantitative-temporal-spatial 70.4
## 5 abstract emotional 70.1
## 6 concrete animate or organic 69.4# Other contribution:
df %>%
group_by(spellout) %>%
summarize(other = mean(other_contribution)) %>%
arrange(desc(other))## # A tibble: 6 × 2
## spellout other
## <chr> <dbl>
## 1 abstract quantitative-temporal-spatial 69.5
## 2 abstract emotional 69.4
## 3 concrete animate or organic 69.1
## 4 concrete inanimate or inorganic 68.9
## 5 abstract self-sociality 68.4
## 6 abstract philosophical-spiritual 67.2“Philosophical-spiritual” is actually least high on other contribution. “Self-sociality” is high on self contribution, but emotional not so much. Overall, the average differences between these categories are relatively small.
Calculate IOS as a function of category and
spellout:
# Abstract versus concrete:
df %>%
group_by(category) %>%
summarize(M = mean(IOS))## # A tibble: 2 × 2
## category M
## <fct> <dbl>
## 1 concrete 3.28
## 2 abstract 3.27# Different sub groups:
df %>%
group_by(subcluster) %>%
summarize(M = mean(IOS)) %>%
arrange(desc(M))## # A tibble: 6 × 2
## subcluster M
## <fct> <dbl>
## 1 EM 3.38
## 2 Conc_in 3.29
## 3 PSTQ 3.29
## 4 Conc_an 3.28
## 5 PS 3.19
## 6 SS 3.18Raw descriptive correlation between covariates:
# Extract covariates into one object:
covs <- df %>%
select(pleasantness:other_contribution)
# Perform pairwise correlations for all covariates:
round(cor(covs), 2)## pleasantness commitment intimacy difficulty
## pleasantness 1.00 0.54 0.53 -0.37
## commitment 0.54 1.00 0.53 -0.18
## intimacy 0.53 0.53 1.00 -0.23
## difficulty -0.37 -0.18 -0.23 1.00
## self_contribution 0.45 0.64 0.44 -0.21
## other_contribution 0.59 0.54 0.43 -0.19
## self_contribution other_contribution
## pleasantness 0.45 0.59
## commitment 0.64 0.54
## intimacy 0.44 0.43
## difficulty -0.21 -0.19
## self_contribution 1.00 0.64
## other_contribution 0.64 1.00The highest correlations are between self_contribution
and commitment, followed by other_contribution
and pleasantness.
For the description of IOS as a function of the different covariates, I think it would be most intuitive to talk about the means of the highest and lowest scale points, as well as perhaps report Spearman’s rho. Let’s do that for each covariate in turn.
Pleasantness:
df %>%
group_by(IOS) %>%
summarize(M = mean(pleasantness))## # A tibble: 6 × 2
## IOS M
## <dbl> <dbl>
## 1 1 36.8
## 2 2 55.6
## 3 3 66.9
## 4 4 72.6
## 5 5 82.4
## 6 6 89.7with(df, cor(IOS, pleasantness, method = 'spearman'))## [1] 0.5265202Commitment:
df %>%
group_by(IOS) %>%
summarize(M = mean(commitment))## # A tibble: 6 × 2
## IOS M
## <dbl> <dbl>
## 1 1 64.4
## 2 2 69.1
## 3 3 72.6
## 4 4 74.0
## 5 5 80.1
## 6 6 83.6with(df, cor(IOS, commitment, method = 'spearman'))## [1] 0.2232285Intimacy:
df %>%
group_by(IOS) %>%
summarize(M = mean(intimacy))## # A tibble: 6 × 2
## IOS M
## <dbl> <dbl>
## 1 1 52.6
## 2 2 57.2
## 3 3 64.2
## 4 4 59.7
## 5 5 72.1
## 6 6 79.9with(df, cor(IOS, intimacy, method = 'spearman'))## [1] 0.2034185Difficulty:
df %>%
group_by(IOS) %>%
summarize(M = mean(difficulty, na.rm = TRUE))## # A tibble: 6 × 2
## IOS M
## <dbl> <dbl>
## 1 1 44.3
## 2 2 34.7
## 3 3 32.0
## 4 4 30.1
## 5 5 22.3
## 6 6 15.8with(df, cor(IOS, difficulty,
method = 'spearman',
use = 'complete.obs'))## [1] -0.2375146Self-contribution:
df %>%
group_by(IOS) %>%
summarize(M = mean(self_contribution, na.rm = TRUE))## # A tibble: 6 × 2
## IOS M
## <dbl> <dbl>
## 1 1 67.7
## 2 2 67.2
## 3 3 68.7
## 4 4 70.8
## 5 5 76.0
## 6 6 81.5with(df, cor(IOS, self_contribution,
method = 'spearman',
use = 'complete.obs'))## [1] 0.1914012Other-contribution:
df %>%
group_by(IOS) %>%
summarize(M = mean(other_contribution, na.rm = TRUE))## # A tibble: 6 × 2
## IOS M
## <dbl> <dbl>
## 1 1 60.2
## 2 2 63.6
## 3 3 68.0
## 4 4 71.1
## 5 5 75.2
## 6 6 82.2with(df, cor(IOS, other_contribution,
method = 'spearman',
use = 'complete.obs'))## [1] 0.25675626 Data visualization
Make a plot of IOS as a function of
category (= concept type, abstract v
concrete).
# Plot core:
category_ios_p <- df %>%
count(IOS, category) %>%
ggplot(aes(x = IOS, y = n, fill = category)) +
geom_col(position = 'dodge', width = 0.7,
col = 'black', size = 0.3)## Warning: Using `size` aesthetic for lines was deprecated in ggplot2 3.4.0.
## ℹ Please use `linewidth` instead.
## This warning is displayed once every 8 hours.
## Call `lifecycle::last_lifecycle_warnings()` to see where this warning was
## generated.# Scales and axes:
category_ios_p <- category_ios_p +
scale_fill_manual(values = c('grey55', 'purple2')) +
scale_x_continuous(expand = c(0, 0),
limits = c(0, 7),
breaks = 1:6) +
scale_y_continuous(expand = c(0, 0),
limits = c(0, 160),
breaks = seq(0, 160, 20)) +
ylab('Number of responses') +
xlab('IOS (self-other inclusion test)')
# Cosmetic tweaking:
category_ios_p <- category_ios_p +
theme_classic() +
theme(legend.position = 'top',
legend.title = element_blank(),
axis.title = element_text(face = 'bold',
size = 12.5),
axis.title.x = element_text(margin = margin(t = 6.5)),
axis.title.y = element_text(margin = margin(r = 10)))
# Show in markdown and save in folder:
category_ios_p
ggsave(plot = category_ios_p,
filename = '../figures_E2/category_ios_E2.pdf',
width = 5, height = 3.5)Make a plot of this with a facet wrap for the median split:
# Plot core:
median_split_p <- df %>%
count(IOS, other_cat, category) %>%
ggplot(aes(x = IOS, y = n, fill = category)) +
geom_bar(position = 'fill', width = 0.7,
stat = 'identity',
col = 'black', size = 0.3) +
facet_wrap(~other_cat, ncol = 2)
# Scales and axes:
median_split_p <- median_split_p +
scale_fill_manual(values = c('goldenrod3', 'steelblue')) +
scale_y_continuous(expand = c(0, 0)) +
ylab('Proportion') +
xlab('IOS (self-other inclusion test)')
# Cosmetic tweaking:
median_split_p <- median_split_p +
theme_classic() +
theme(legend.position = 'top',
legend.title = element_blank(),
axis.title = element_text(face = 'bold',
size = 12.5),
axis.title.x = element_text(margin = margin(t = 6.5)),
axis.title.y = element_text(margin = margin(r = 10)),
plot.margin = margin(r = 100))
# Show in markdown and save in folder:
median_split_p
ggsave(plot = median_split_p,
filename = '../figures_E2/median_split_E2_p.pdf',
width = 7, height = 3)Copy and paste the code from Experiment 1 here to reproduce the bin plot:
df <- mutate(df,
other_bin2 = cut_number(other_contribution, 4))
# Redo the averages:
bin_avgs <- df %>%
group_by(other_bin2, category) %>%
summarize(IOS_M = mean(IOS),
IOS_SD = sd(IOS))## `summarise()` has grouped output by 'other_bin2'. You can override using the
## `.groups` argument.# Append counts so that we can compute simple standard errors of the mean:
bin_counts <- df %>%
count(other_bin2, category)
# Join together:
bin_avgs <- left_join(bin_avgs, bin_counts)## Joining with `by = join_by(other_bin2, category)`# Compute standard errors:
bin_avgs <- mutate(bin_avgs,
SE = IOS_SD / sqrt(n),
lower = IOS_M - SE,
upper = IOS_M + SE,
lower_CI = IOS_M - 1.96 * SE,
upper_CI = IOS_M + 1.96 * SE)Let’s do that new bin plot:
# Plot core:
bin_p <- bin_avgs %>%
ggplot(aes(x = other_bin2, y = IOS_M,
color = category, group = category)) +
geom_line(size = 0.8) +
geom_point(pch = 15, size = 2,
position = position_dodge(width = 0.1)) +
geom_errorbar(aes(ymin = lower_CI, ymax = upper_CI),
width = 0,
position = position_dodge(width = 0.1))
# Scales and axes:
bin_p <- bin_p +
scale_color_manual(values = c('goldenrod3', 'steelblue')) +
scale_y_continuous(expand = c(0, 0),
limits = c(2, 4.5),
breaks = seq(2, 4.5, 0.5)) +
ylab('IOS mean') +
xlab('Other contribution (binned)') +
annotate(geom = 'text',
label = 'concrete concepts',
color = 'goldenrod3',
x = 0.7, y = 3.25,
hjust = 0, size = 3) +
annotate(geom = 'text',
label = 'abstract concepts',
color = 'steelblue',
x = 0.7, y = 2.51,
hjust = 0, size = 3)
# Cosmetic tweaking:
bin_p <- bin_p +
theme_classic() +
theme(legend.position = 'none',
legend.title = element_blank(),
axis.title = element_text(face = 'bold',
size = 12.5),
axis.title.x = element_text(margin = margin(t = 6.5)),
axis.title.y = element_text(margin = margin(r = 10)))
# Show in markdown and save in folder:
bin_p
ggsave(plot = bin_p,
filename = '../figures_E2/IOS_equal_bin_plot.pdf',
width = 4.5, height = 3.4)7 Data visualization: covariates, and covariates with IOS
Scatter plot matrix for covariates:
# Setings for diagonal:
diag_wrap <- wrap("densityDiag", alpha = 0.5,
fill = 'steelblue')
# Plot core:
scatter_p <- ggpairs(covs,
aes(alpha = 0.5),
diag = list(continuous = diag_wrap))
# Cosmetics:
scatter_p <- scatter_p +
theme_minimal()
# Show in markdown and save in folder:
scatter_p
ggsave(plot = scatter_p,
filename = '../figures_E2/covariate_matrix_E2.pdf',
width = 8, height = 8)Pleasantness and IOS:
# Plot core:
pleasant_joy_p <- df %>%
ggplot(aes(x = pleasantness, y = factor(IOS))) +
geom_density_ridges(fill = 'steelblue',
jittered_points = TRUE,
position = position_points_jitter(width = 0.05,
height = 0),
point_shape = '|', point_size = 2,
point_alpha = 1, alpha = 0.7)
# Scales and axes:
pleasant_joy_p <- pleasant_joy_p +
ylab('IOS\n(inclusion of other scale)') +
xlab('Pleasantness') +
scale_x_continuous(breaks = seq(0, 100, 20),
limits = c(-20, +120))
# Cosmetic tweaking:
pleasant_joy_p <- pleasant_joy_p +
theme_classic() +
theme(legend.position = 'none',
legend.title = element_blank(),
axis.title = element_text(face = 'bold',
size = 12.5),
axis.title.x = element_text(margin = margin(t = 6.5)),
axis.title.y = element_text(margin = margin(r = 10)))
# Show in markdown and save in folder:
pleasant_joy_p## Picking joint bandwidth of 5.67
ggsave(plot = pleasant_joy_p,
filename = '../figures_E2/pleasantness_joy_E2.pdf',
width = 5, height = 3.5)## Picking joint bandwidth of 5.67Commitment and IOS:
# Plot core:
commit_joy_p <- df %>%
ggplot(aes(x = commitment, y = factor(IOS))) +
geom_density_ridges(fill = 'steelblue',
jittered_points = TRUE,
position = position_points_jitter(width = 0.05,
height = 0),
point_shape = '|', point_size = 2,
point_alpha = 1, alpha = 0.7)
# Scales and axes:
commit_joy_p <- commit_joy_p +
ylab('IOS\n(inclusion of other scale)') +
xlab('Commitment') +
scale_x_continuous(breaks = seq(0, 100, 20),
limits = c(-20, +120))
# Cosmetic tweaking:
commit_joy_p <- commit_joy_p +
theme_classic() +
theme(legend.position = 'none',
legend.title = element_blank(),
axis.title = element_text(face = 'bold',
size = 12.5),
axis.title.x = element_text(margin = margin(t = 6.5)),
axis.title.y = element_text(margin = margin(r = 10)))
# Show in markdown and save in folder:
commit_joy_p## Picking joint bandwidth of 6.22## Warning: Removed 1 rows containing non-finite values (`stat_density_ridges()`).
ggsave(plot = commit_joy_p,
filename = '../figures_E2/commitment_joy_E2.pdf',
width = 4.5, height = 4)## Picking joint bandwidth of 6.22## Warning: Removed 1 rows containing non-finite values (`stat_density_ridges()`).Intimacy and IOS:
# Plot core:
intimate_joy_p <- df %>%
ggplot(aes(x = intimacy, y = factor(IOS))) +
geom_density_ridges(fill = 'steelblue',
jittered_points = TRUE,
position = position_points_jitter(width = 0.05,
height = 0),
point_shape = '|', point_size = 2,
point_alpha = 1, alpha = 0.7)
# Scales and axes:
intimate_joy_p <- intimate_joy_p +
ylab('IOS\n(inclusion of other scale)') +
xlab('Intimacy') +
scale_x_continuous(breaks = seq(0, 100, 20),
limits = c(-20, +120))
# Cosmetic tweaking:
intimate_joy_p <- intimate_joy_p +
theme_classic() +
theme(legend.position = 'none',
legend.title = element_blank(),
axis.title = element_text(face = 'bold',
size = 12.5),
axis.title.x = element_text(margin = margin(t = 6.5)),
axis.title.y = element_text(margin = margin(r = 10)))
# Show in markdown and save in folder:
intimate_joy_p## Picking joint bandwidth of 8.47
ggsave(plot = intimate_joy_p,
filename = '../figures_E2/intimacy_joy_E2.pdf',
width = 4.5, height = 4)## Picking joint bandwidth of 8.47Difficulty and IOS:
# Plot core:
difficult_joy_p <- df %>%
ggplot(aes(x = difficulty, y = factor(IOS)))+
geom_density_ridges(fill = 'steelblue',
jittered_points = TRUE,
position = position_points_jitter(width = 0.05,
height = 0),
point_shape = '|', point_size = 2,
point_alpha = 1, alpha = 0.7)
# Scales and axes:
difficult_joy_p <- difficult_joy_p +
ylab('IOS\n(inclusion of other scale)') +
xlab('Difficulty') +
scale_x_continuous(breaks = seq(0, 100, 20),
limits = c(-20, +120))
# Cosmetic tweaking:
difficult_joy_p <- difficult_joy_p +
theme_classic() +
theme(legend.position = 'none',
legend.title = element_blank(),
axis.title = element_text(face = 'bold',
size = 12.5),
axis.title.x = element_text(margin = margin(t = 6.5)),
axis.title.y = element_text(margin = margin(r = 10)))
# Show in markdown and save in folder:
difficult_joy_p## Picking joint bandwidth of 7.04
ggsave(plot = difficult_joy_p,
filename = '../figures_E2/difficulty_joy_E2.pdf',
width = 4.5, height = 4)## Picking joint bandwidth of 7.04Self contribution and IOS:
# Plot core:
self_joy_p <- df %>%
ggplot(aes(x = self_contribution, y = factor(IOS))) +
geom_density_ridges(fill = 'steelblue',
jittered_points = TRUE,
position = position_points_jitter(width = 0.05,
height = 0),
point_shape = '|', point_size = 2,
point_alpha = 1, alpha = 0.7)
# Scales and axes:
self_joy_p <- self_joy_p +
ylab('IOS\n(inclusion of other scale)') +
xlab('Self contribution') +
scale_x_continuous(breaks = seq(0, 100, 20),
limits = c(-20, +120))
# Cosmetic tweaking:
self_joy_p <- self_joy_p +
theme_classic() +
theme(legend.position = 'none',
legend.title = element_blank(),
axis.title = element_text(face = 'bold',
size = 12.5),
axis.title.x = element_text(margin = margin(t = 6.5)),
axis.title.y = element_text(margin = margin(r = 10)))
# Show in markdown and save in folder:
self_joy_p## Picking joint bandwidth of 6.46## Warning: Removed 1 rows containing non-finite values (`stat_density_ridges()`).
ggsave(plot = self_joy_p,
filename = '../figures_E2/self_joy_E2.pdf',
width = 4.5, height = 4)## Picking joint bandwidth of 6.46## Warning: Removed 1 rows containing non-finite values (`stat_density_ridges()`).Other contribution and IOS:
# Plot core:
other_joy_p <- df %>%
ggplot(aes(x = other_contribution, y = factor(IOS))) +
geom_density_ridges(fill = 'steelblue',
jittered_points = TRUE,
position = position_points_jitter(width = 0.05,
height = 0),
point_shape = '|', point_size = 2,
point_alpha = 1, alpha = 0.7)
# Scales and axes:
other_joy_p <- other_joy_p +
ylab('IOS\n(inclusion of other scale)') +
xlab('Other contribution') +
scale_x_continuous(breaks = seq(0, 100, 20),
limits = c(-20, +120))
# Cosmetic tweaking:
other_joy_p <- other_joy_p +
theme_classic() +
theme(legend.position = 'none',
legend.title = element_blank(),
axis.title = element_text(face = 'bold',
size = 12.5),
axis.title.x = element_text(margin = margin(t = 6.5)),
axis.title.y = element_text(margin = margin(r = 10)))
# Show in markdown and save in folder:
other_joy_p## Picking joint bandwidth of 6.53
ggsave(plot = other_joy_p,
filename = '../figures_E2/other_joy_E2.pdf',
width = 4.5, height = 4)## Picking joint bandwidth of 6.53Make a plot matrix out of all of these:
# Define layout matrix:
my_layout <- matrix(c(1, 2, 3,
4, 5, 6),
byrow = TRUE, ncol = 3)
# Change titles:
commit_joy_p <- commit_joy_p +
ylab(NULL)
intimate_joy_p <- intimate_joy_p +
ylab(NULL)
self_joy_p <- self_joy_p +
ylab(NULL)
other_joy_p <- other_joy_p +
ylab(NULL)
# Show:
grid.arrange(pleasant_joy_p, commit_joy_p, intimate_joy_p,
difficult_joy_p, self_joy_p, other_joy_p,
layout_matrix = my_layout)
# Save:
all_joy <- arrangeGrob(pleasant_joy_p, commit_joy_p, intimate_joy_p,
difficult_joy_p, self_joy_p, other_joy_p,
layout_matrix = my_layout)
# Save:
all_joy <- arrangeGrob(pleasant_joy_p, commit_joy_p, intimate_joy_p,
difficult_joy_p, self_joy_p, other_joy_p,
layout_matrix = my_layout)
ggsave(all_joy, file = '../figures_E2/all_covariate_joy_E2.pdf',
width = 12, height = 6)8 Data visualization: scatterplots of covariates with closeness
Scatterplot matrix of all variables. First, let’s start with pleasantness:
pleasant_scatter <- df |>
ggplot(aes(x = pleasantness, y = closeness)) +
geom_smooth(method = 'lm', col = 'purple',
se = FALSE, size = 1.5) +
geom_point()
# Scales and axes:
pleasant_scatter <- pleasant_scatter +
ylab('Closeness') +
xlab('Pleasantness') +
scale_x_continuous(breaks = seq(0, 100, 20),
limits = c(-5, +105))
# Cosmetic tweaking:
pleasant_scatter <- pleasant_scatter +
theme_classic() +
theme(legend.position = 'none',
legend.title = element_blank(),
axis.title = element_text(face = 'bold',
size = 12.5),
axis.title.x = element_text(margin = margin(t = 6.5)),
axis.title.y = element_text(margin = margin(r = 10)))
# Show and save:
pleasant_scatter## `geom_smooth()` using formula = 'y ~ x'
ggsave(filename = '../figures_E2/E2_pleasant_scatter.pdf', plot = pleasant_scatter,
width = 4.5, height = 4)## `geom_smooth()` using formula = 'y ~ x'ggsave(filename = '../figures_E2/E2_pleasant_scatter.png', plot = pleasant_scatter,
width = 4.5, height = 4)## `geom_smooth()` using formula = 'y ~ x'Second, commitment:
commitment_scatter <- df |>
ggplot(aes(x = commitment, y = closeness)) +
geom_smooth(method = 'lm', col = 'purple',
se = FALSE, size = 1.5) +
geom_point()
# Scales and axes:
commitment_scatter <- commitment_scatter +
ylab('Closeness') +
xlab('Pleasantness') +
scale_x_continuous(breaks = seq(0, 100, 20),
limits = c(-5, +105))
# Cosmetic tweaking:
commitment_scatter <- commitment_scatter +
theme_classic() +
theme(legend.position = 'none',
legend.title = element_blank(),
axis.title = element_text(face = 'bold',
size = 12.5),
axis.title.x = element_text(margin = margin(t = 6.5)),
axis.title.y = element_text(margin = margin(r = 10)))
# Show and save:
commitment_scatter## `geom_smooth()` using formula = 'y ~ x'## Warning: Removed 1 rows containing non-finite values (`stat_smooth()`).## Warning: Removed 1 rows containing missing values (`geom_point()`).
ggsave(filename = '../figures_E2/E2_commitment_scatter.pdf',
plot = commitment_scatter,
width = 4.5, height = 4)## `geom_smooth()` using formula = 'y ~ x'## Warning: Removed 1 rows containing non-finite values (`stat_smooth()`).
## Removed 1 rows containing missing values (`geom_point()`).ggsave(filename = '../figures_E2/E2_commitment_scatter.png',
plot = commitment_scatter,
width = 4.5, height = 4)## `geom_smooth()` using formula = 'y ~ x'## Warning: Removed 1 rows containing non-finite values (`stat_smooth()`).
## Removed 1 rows containing missing values (`geom_point()`).Third, intimacy:
intimacy_scatter <- df |>
ggplot(aes(x = intimacy, y = closeness)) +
geom_smooth(method = 'lm', col = 'purple',
se = FALSE, size = 1.5) +
geom_point()
# Scales and axes:
intimacy_scatter <- intimacy_scatter +
ylab('Closeness') +
xlab('Pleasantness') +
scale_x_continuous(breaks = seq(0, 100, 20),
limits = c(-5, +105))
# Cosmetic tweaking:
intimacy_scatter <- intimacy_scatter +
theme_classic() +
theme(legend.position = 'none',
legend.title = element_blank(),
axis.title = element_text(face = 'bold',
size = 12.5),
axis.title.x = element_text(margin = margin(t = 6.5)),
axis.title.y = element_text(margin = margin(r = 10)))
# Show and save:
intimacy_scatter## `geom_smooth()` using formula = 'y ~ x'
ggsave(filename = '../figures_E2/E2_intimacy_scatter.pdf',
plot = intimacy_scatter,
width = 4.5, height = 4)## `geom_smooth()` using formula = 'y ~ x'ggsave(filename = '../figures_E2/E2_intimacy_scatter.png',
plot = intimacy_scatter,
width = 4.5, height = 4)## `geom_smooth()` using formula = 'y ~ x'Fourth, difficulty:
difficulty_scatter <- df |>
ggplot(aes(x = difficulty, y = closeness)) +
geom_smooth(method = 'lm', col = 'purple',
se = FALSE, size = 1.5) +
geom_point()
# Scales and axes:
difficulty_scatter <- difficulty_scatter +
ylab('Closeness') +
xlab('Pleasantness') +
scale_x_continuous(breaks = seq(0, 100, 20),
limits = c(-5, +105))
# Cosmetic tweaking:
difficulty_scatter <- difficulty_scatter +
theme_classic() +
theme(legend.position = 'none',
legend.title = element_blank(),
axis.title = element_text(face = 'bold',
size = 12.5),
axis.title.x = element_text(margin = margin(t = 6.5)),
axis.title.y = element_text(margin = margin(r = 10)))
# Show and save:
difficulty_scatter## `geom_smooth()` using formula = 'y ~ x'
ggsave(filename = '../figures_E2/E2_difficulty_scatter.pdf',
plot = difficulty_scatter,
width = 4.5, height = 4)## `geom_smooth()` using formula = 'y ~ x'ggsave(filename = '../figures_E2/E2_difficulty_scatter.png',
plot = difficulty_scatter,
width = 4.5, height = 4)## `geom_smooth()` using formula = 'y ~ x'Fifth, self-contribution:
self_contribution_scatter <- df |>
ggplot(aes(x = self_contribution, y = closeness)) +
geom_smooth(method = 'lm', col = 'purple',
se = FALSE, size = 1.5) +
geom_point()
# Scales and axes:
self_contribution_scatter <- self_contribution_scatter +
ylab('Closeness') +
xlab('Pleasantness') +
scale_x_continuous(breaks = seq(0, 100, 20),
limits = c(-5, +105))
# Cosmetic tweaking:
self_contribution_scatter <- self_contribution_scatter +
theme_classic() +
theme(legend.position = 'none',
legend.title = element_blank(),
axis.title = element_text(face = 'bold',
size = 12.5),
axis.title.x = element_text(margin = margin(t = 6.5)),
axis.title.y = element_text(margin = margin(r = 10)))
# Show and save:
self_contribution_scatter## `geom_smooth()` using formula = 'y ~ x'## Warning: Removed 1 rows containing non-finite values (`stat_smooth()`).## Warning: Removed 1 rows containing missing values (`geom_point()`).
ggsave(filename = '../figures_E2/E2_self_contribution_scatter.pdf',
plot = self_contribution_scatter,
width = 4.5, height = 4)## `geom_smooth()` using formula = 'y ~ x'## Warning: Removed 1 rows containing non-finite values (`stat_smooth()`).
## Removed 1 rows containing missing values (`geom_point()`).ggsave(filename = '../figures_E2/E2_self_contribution_scatter.png',
plot = self_contribution_scatter,
width = 4.5, height = 4)## `geom_smooth()` using formula = 'y ~ x'## Warning: Removed 1 rows containing non-finite values (`stat_smooth()`).
## Removed 1 rows containing missing values (`geom_point()`).Sixth, other-contribution:
other_contribution_scatter <- df |>
ggplot(aes(x = other_contribution, y = closeness)) +
geom_smooth(method = 'lm', col = 'purple',
se = FALSE, size = 1.5) +
geom_point()
# Scales and axes:
other_contribution_scatter <- other_contribution_scatter +
ylab('Closeness') +
xlab('Pleasantness') +
scale_x_continuous(breaks = seq(0, 100, 20),
limits = c(-5, +105))
# Cosmetic tweaking:
other_contribution_scatter <- other_contribution_scatter +
theme_classic() +
theme(legend.position = 'none',
legend.title = element_blank(),
axis.title = element_text(face = 'bold',
size = 12.5),
axis.title.x = element_text(margin = margin(t = 6.5)),
axis.title.y = element_text(margin = margin(r = 10)))
# Show and save:
other_contribution_scatter## `geom_smooth()` using formula = 'y ~ x'
ggsave(filename = '../figures_E2/E2_other_contribution_scatter.pdf',
plot = other_contribution_scatter,
width = 4.5, height = 4)## `geom_smooth()` using formula = 'y ~ x'ggsave(filename = '../figures_E2/E2_other_contribution_scatter.png',
plot = other_contribution_scatter,
width = 4.5, height = 4)## `geom_smooth()` using formula = 'y ~ x'Put everything together into a big plot matrix:
# Define layout matrix:
my_layout <- matrix(c(1, 2, 3,
4, 5, 6),
byrow = TRUE, ncol = 3)
# Change titles:
commitment_scatter <- commitment_scatter +
ylab(NULL)
intimacy_scatter <- intimacy_scatter +
ylab(NULL)
self_contribution_scatter <- self_contribution_scatter +
ylab(NULL)
other_contribution_scatter <- other_contribution_scatter +
ylab(NULL)
# Show:
grid.arrange(pleasant_scatter, commitment_scatter, intimacy_scatter,
difficulty_scatter, self_contribution_scatter, other_contribution_scatter,
layout_matrix = my_layout)
# Save:
all_joy <- arrangeGrob(pleasant_scatter, commitment_scatter, intimacy_scatter,
difficulty_scatter, self_contribution_scatter, other_contribution_scatter,
layout_matrix = my_layout)
ggsave(all_joy, file = '../figures_E2/all_covariate_closeness.pdf',
width = 12, height = 6)
ggsave(all_joy, file = '../figures_E2/all_covariate_closeness.png',
width = 12, height = 6)9 Covariate models
Make a model of all covariates on IOS:
covariates_IOS_mdl <- brm(IOS ~
# Fixed effects:
1 +
pleasantness +
commitment +
intimacy +
difficulty +
self_contribution +
other_contribution +
# Random effects:
(1|participant) +
(0 + pleasantness|participant) +
(0 + commitment|participant) +
(0 + intimacy|participant) +
(0 + difficulty|participant) +
(0 + self_contribution|participant) +
(0 + other_contribution|participant) +
(1|word),
# General stuff:
data = df,
family = cumulative,
# MCMC settings:
seed = 42,
cores = 4,
iter = 6000,
warmup = 3000,
control = list(adapt_delta = 0.9))
# Save model:
save(covariates_IOS_mdl, file = '../models_E2/covariates_IOS_mdl.Rdata')Load:
load('../models_E2/covariates_IOS_mdl.Rdata')Show priors:
prior_summary(covariates_IOS_mdl)## prior class coef group resp dpar nlpar
## (flat) b
## (flat) b commitment
## (flat) b difficulty
## (flat) b intimacy
## (flat) b other_contribution
## (flat) b pleasantness
## (flat) b self_contribution
## student_t(3, 0, 2.5) Intercept
## student_t(3, 0, 2.5) Intercept 1
## student_t(3, 0, 2.5) Intercept 2
## student_t(3, 0, 2.5) Intercept 3
## student_t(3, 0, 2.5) Intercept 4
## student_t(3, 0, 2.5) Intercept 5
## student_t(3, 0, 2.5) sd
## student_t(3, 0, 2.5) sd participant
## student_t(3, 0, 2.5) sd commitment participant
## student_t(3, 0, 2.5) sd difficulty participant
## student_t(3, 0, 2.5) sd Intercept participant
## student_t(3, 0, 2.5) sd intimacy participant
## student_t(3, 0, 2.5) sd other_contribution participant
## student_t(3, 0, 2.5) sd pleasantness participant
## student_t(3, 0, 2.5) sd self_contribution participant
## student_t(3, 0, 2.5) sd word
## student_t(3, 0, 2.5) sd Intercept word
## lb ub source
## default
## (vectorized)
## (vectorized)
## (vectorized)
## (vectorized)
## (vectorized)
## (vectorized)
## default
## (vectorized)
## (vectorized)
## (vectorized)
## (vectorized)
## (vectorized)
## 0 default
## 0 (vectorized)
## 0 (vectorized)
## 0 (vectorized)
## 0 (vectorized)
## 0 (vectorized)
## 0 (vectorized)
## 0 (vectorized)
## 0 (vectorized)
## 0 (vectorized)
## 0 (vectorized)Check posterior predictive checks of the mixed beta regression:
pp_check(covariates_IOS_mdl, ndraws = 100, type = 'ecdf_overlay')
Check this model:
covariates_IOS_mdl## Family: cumulative
## Links: mu = logit; disc = identity
## Formula: IOS ~ 1 + pleasantness + commitment + intimacy + difficulty + self_contribution + other_contribution + (1 | participant) + (0 + pleasantness | participant) + (0 + commitment | participant) + (0 + intimacy | participant) + (0 + difficulty | participant) + (0 + self_contribution | participant) + (0 + other_contribution | participant) + (1 | word)
## Data: df (Number of observations: 1032)
## Draws: 4 chains, each with iter = 6000; warmup = 3000; thin = 1;
## total post-warmup draws = 12000
##
## Group-Level Effects:
## ~participant (Number of levels: 129)
## Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS
## sd(Intercept) 1.40 0.48 0.27 2.24 1.00 1197
## sd(pleasantness) 0.02 0.01 0.01 0.03 1.00 1945
## sd(commitment) 0.02 0.01 0.00 0.03 1.01 1172
## sd(intimacy) 0.02 0.01 0.00 0.03 1.00 1799
## sd(difficulty) 0.01 0.01 0.00 0.03 1.00 2022
## sd(self_contribution) 0.01 0.01 0.00 0.02 1.00 1941
## sd(other_contribution) 0.01 0.01 0.00 0.03 1.00 1513
## Tail_ESS
## sd(Intercept) 1275
## sd(pleasantness) 1568
## sd(commitment) 2683
## sd(intimacy) 2095
## sd(difficulty) 3102
## sd(self_contribution) 3978
## sd(other_contribution) 4313
##
## ~word (Number of levels: 32)
## Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
## sd(Intercept) 0.09 0.07 0.00 0.24 1.00 7830 6551
##
## Population-Level Effects:
## Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
## Intercept[1] 0.79 0.60 -0.39 1.98 1.00 14619 9690
## Intercept[2] 4.93 0.62 3.74 6.16 1.00 12938 10156
## Intercept[3] 8.07 0.67 6.80 9.40 1.00 11378 9852
## Intercept[4] 10.63 0.72 9.26 12.07 1.00 10521 9623
## Intercept[5] 13.49 0.79 11.99 15.08 1.00 9927 9165
## pleasantness 0.09 0.01 0.08 0.11 1.00 9954 9549
## commitment 0.01 0.01 -0.01 0.02 1.00 11038 9419
## intimacy 0.01 0.00 0.00 0.02 1.00 16090 9585
## difficulty -0.01 0.00 -0.02 -0.00 1.00 17458 9863
## self_contribution -0.00 0.01 -0.02 0.01 1.00 11348 8346
## other_contribution 0.00 0.01 -0.01 0.01 1.00 15542 9568
##
## Family Specific Parameters:
## Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
## disc 1.00 0.00 1.00 1.00 NA NA NA
##
## Draws were sampled using sampling(NUTS). For each parameter, Bulk_ESS
## and Tail_ESS are effective sample size measures, and Rhat is the potential
## scale reduction factor on split chains (at convergence, Rhat = 1).Test all hypotheses from the covariate model:
hypothesis(covariates_IOS_mdl, 'pleasantness > 0')## Hypothesis Tests for class b:
## Hypothesis Estimate Est.Error CI.Lower CI.Upper Evid.Ratio Post.Prob
## 1 (pleasantness) > 0 0.09 0.01 0.08 0.1 Inf 1
## Star
## 1 *
## ---
## 'CI': 90%-CI for one-sided and 95%-CI for two-sided hypotheses.
## '*': For one-sided hypotheses, the posterior probability exceeds 95%;
## for two-sided hypotheses, the value tested against lies outside the 95%-CI.
## Posterior probabilities of point hypotheses assume equal prior probabilities.hypothesis(covariates_IOS_mdl, 'commitment > 0')## Hypothesis Tests for class b:
## Hypothesis Estimate Est.Error CI.Lower CI.Upper Evid.Ratio Post.Prob
## 1 (commitment) > 0 0.01 0.01 0 0.02 7.4 0.88
## Star
## 1
## ---
## 'CI': 90%-CI for one-sided and 95%-CI for two-sided hypotheses.
## '*': For one-sided hypotheses, the posterior probability exceeds 95%;
## for two-sided hypotheses, the value tested against lies outside the 95%-CI.
## Posterior probabilities of point hypotheses assume equal prior probabilities.hypothesis(covariates_IOS_mdl, 'intimacy > 0')## Hypothesis Tests for class b:
## Hypothesis Estimate Est.Error CI.Lower CI.Upper Evid.Ratio Post.Prob Star
## 1 (intimacy) > 0 0.01 0 0 0.02 65.3 0.98 *
## ---
## 'CI': 90%-CI for one-sided and 95%-CI for two-sided hypotheses.
## '*': For one-sided hypotheses, the posterior probability exceeds 95%;
## for two-sided hypotheses, the value tested against lies outside the 95%-CI.
## Posterior probabilities of point hypotheses assume equal prior probabilities.hypothesis(covariates_IOS_mdl, 'difficulty < 0')## Hypothesis Tests for class b:
## Hypothesis Estimate Est.Error CI.Lower CI.Upper Evid.Ratio Post.Prob
## 1 (difficulty) < 0 -0.01 0 -0.02 0 72.17 0.99
## Star
## 1 *
## ---
## 'CI': 90%-CI for one-sided and 95%-CI for two-sided hypotheses.
## '*': For one-sided hypotheses, the posterior probability exceeds 95%;
## for two-sided hypotheses, the value tested against lies outside the 95%-CI.
## Posterior probabilities of point hypotheses assume equal prior probabilities.hypothesis(covariates_IOS_mdl, 'self_contribution > 0')## Hypothesis Tests for class b:
## Hypothesis Estimate Est.Error CI.Lower CI.Upper Evid.Ratio
## 1 (self_contribution) > 0 0 0.01 -0.01 0.01 0.56
## Post.Prob Star
## 1 0.36
## ---
## 'CI': 90%-CI for one-sided and 95%-CI for two-sided hypotheses.
## '*': For one-sided hypotheses, the posterior probability exceeds 95%;
## for two-sided hypotheses, the value tested against lies outside the 95%-CI.
## Posterior probabilities of point hypotheses assume equal prior probabilities.hypothesis(covariates_IOS_mdl, 'other_contribution > 0')## Hypothesis Tests for class b:
## Hypothesis Estimate Est.Error CI.Lower CI.Upper Evid.Ratio
## 1 (other_contribution) > 0 0 0.01 -0.01 0.01 1.5
## Post.Prob Star
## 1 0.6
## ---
## 'CI': 90%-CI for one-sided and 95%-CI for two-sided hypotheses.
## '*': For one-sided hypotheses, the posterior probability exceeds 95%;
## for two-sided hypotheses, the value tested against lies outside the 95%-CI.
## Posterior probabilities of point hypotheses assume equal prior probabilities.Now closeness as a function of all covariates:
covariates_dist_mdl <- brm(bf(closeness_01 ~
# Fixed effects:
1 +
pleasantness +
commitment +
intimacy +
difficulty +
self_contribution +
other_contribution +
# Random effects:
(1|participant) +
(0 + pleasantness|participant) +
(0 + commitment|participant) +
(0 + intimacy|participant) +
(0 + difficulty|participant) +
(0 + self_contribution|participant) +
(0 + other_contribution|participant) +
(1|word),
# Family-specific parameter (shape):
phi ~ 1),
# General stuff:
data = df,
family = Beta,
# MCMC settings:
init = 0, # doesn't converge otherwise
seed = 42,
cores = 4,
iter = 6000,
warmup = 3000,
control = list(adapt_delta = 0.90))
# Save model:
save(covariates_dist_mdl, file = '../models_E2/covariates_dist_mdl.Rdata')Load:
load('../models_E2/covariates_dist_mdl.Rdata')Show priors:
prior_summary(covariates_dist_mdl)## prior class coef group resp dpar nlpar
## (flat) b
## (flat) b commitment
## (flat) b difficulty
## (flat) b intimacy
## (flat) b other_contribution
## (flat) b pleasantness
## (flat) b self_contribution
## student_t(3, 0, 2.5) Intercept
## student_t(3, 0, 2.5) Intercept phi
## student_t(3, 0, 2.5) sd
## student_t(3, 0, 2.5) sd participant
## student_t(3, 0, 2.5) sd commitment participant
## student_t(3, 0, 2.5) sd difficulty participant
## student_t(3, 0, 2.5) sd Intercept participant
## student_t(3, 0, 2.5) sd intimacy participant
## student_t(3, 0, 2.5) sd other_contribution participant
## student_t(3, 0, 2.5) sd pleasantness participant
## student_t(3, 0, 2.5) sd self_contribution participant
## student_t(3, 0, 2.5) sd word
## student_t(3, 0, 2.5) sd Intercept word
## lb ub source
## default
## (vectorized)
## (vectorized)
## (vectorized)
## (vectorized)
## (vectorized)
## (vectorized)
## default
## default
## 0 default
## 0 (vectorized)
## 0 (vectorized)
## 0 (vectorized)
## 0 (vectorized)
## 0 (vectorized)
## 0 (vectorized)
## 0 (vectorized)
## 0 (vectorized)
## 0 (vectorized)
## 0 (vectorized)Check posterior predictive checks of the mixed beta regression:
pp_check(covariates_dist_mdl,
ndraws = 100, type = 'ecdf_overlay')
Check this model:
covariates_dist_mdl## Warning: There were 1 divergent transitions after warmup. Increasing
## adapt_delta above 0.9 may help. See
## http://mc-stan.org/misc/warnings.html#divergent-transitions-after-warmup## Family: beta
## Links: mu = logit; phi = log
## Formula: closeness_01 ~ 1 + pleasantness + commitment + intimacy + difficulty + self_contribution + other_contribution + (1 | participant) + (0 + pleasantness | participant) + (0 + commitment | participant) + (0 + intimacy | participant) + (0 + difficulty | participant) + (0 + self_contribution | participant) + (0 + other_contribution | participant) + (1 | word)
## phi ~ 1
## Data: df (Number of observations: 1032)
## Draws: 4 chains, each with iter = 6000; warmup = 3000; thin = 1;
## total post-warmup draws = 12000
##
## Group-Level Effects:
## ~participant (Number of levels: 129)
## Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS
## sd(Intercept) 0.79 0.10 0.60 1.00 1.00 3466
## sd(pleasantness) 0.01 0.00 0.01 0.01 1.00 3183
## sd(commitment) 0.01 0.00 0.01 0.01 1.00 3458
## sd(intimacy) 0.01 0.00 0.00 0.01 1.00 3923
## sd(difficulty) 0.01 0.00 0.00 0.01 1.00 3839
## sd(self_contribution) 0.00 0.00 0.00 0.00 1.00 4318
## sd(other_contribution) 0.01 0.00 0.00 0.01 1.00 1428
## Tail_ESS
## sd(Intercept) 6218
## sd(pleasantness) 5441
## sd(commitment) 6062
## sd(intimacy) 4986
## sd(difficulty) 5495
## sd(self_contribution) 6045
## sd(other_contribution) 1200
##
## ~word (Number of levels: 32)
## Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
## sd(Intercept) 0.02 0.02 0.00 0.06 1.00 5094 5573
##
## Population-Level Effects:
## Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
## Intercept -0.49 0.15 -0.79 -0.20 1.00 10118 9756
## phi_Intercept 3.65 0.07 3.52 3.78 1.00 2286 5174
## pleasantness 0.02 0.00 0.01 0.02 1.00 8577 9634
## commitment -0.00 0.00 -0.00 0.00 1.00 8875 9373
## intimacy 0.00 0.00 -0.00 0.00 1.00 9734 9692
## difficulty -0.00 0.00 -0.00 -0.00 1.00 12465 10832
## self_contribution 0.00 0.00 -0.00 0.00 1.00 10569 9290
## other_contribution 0.01 0.00 0.00 0.01 1.00 9479 9751
##
## Draws were sampled using sampling(NUTS). For each parameter, Bulk_ESS
## and Tail_ESS are effective sample size measures, and Rhat is the potential
## scale reduction factor on split chains (at convergence, Rhat = 1).Test all hypotheses from the covariate model:
hypothesis(covariates_dist_mdl, 'pleasantness > 0')## Hypothesis Tests for class b:
## Hypothesis Estimate Est.Error CI.Lower CI.Upper Evid.Ratio Post.Prob
## 1 (pleasantness) > 0 0.02 0 0.01 0.02 Inf 1
## Star
## 1 *
## ---
## 'CI': 90%-CI for one-sided and 95%-CI for two-sided hypotheses.
## '*': For one-sided hypotheses, the posterior probability exceeds 95%;
## for two-sided hypotheses, the value tested against lies outside the 95%-CI.
## Posterior probabilities of point hypotheses assume equal prior probabilities.hypothesis(covariates_dist_mdl, 'commitment > 0')## Hypothesis Tests for class b:
## Hypothesis Estimate Est.Error CI.Lower CI.Upper Evid.Ratio Post.Prob
## 1 (commitment) > 0 0 0 0 0 0.36 0.26
## Star
## 1
## ---
## 'CI': 90%-CI for one-sided and 95%-CI for two-sided hypotheses.
## '*': For one-sided hypotheses, the posterior probability exceeds 95%;
## for two-sided hypotheses, the value tested against lies outside the 95%-CI.
## Posterior probabilities of point hypotheses assume equal prior probabilities.hypothesis(covariates_dist_mdl, 'intimacy > 0')## Hypothesis Tests for class b:
## Hypothesis Estimate Est.Error CI.Lower CI.Upper Evid.Ratio Post.Prob Star
## 1 (intimacy) > 0 0 0 0 0 3.42 0.77
## ---
## 'CI': 90%-CI for one-sided and 95%-CI for two-sided hypotheses.
## '*': For one-sided hypotheses, the posterior probability exceeds 95%;
## for two-sided hypotheses, the value tested against lies outside the 95%-CI.
## Posterior probabilities of point hypotheses assume equal prior probabilities.hypothesis(covariates_dist_mdl, 'difficulty < 0')## Hypothesis Tests for class b:
## Hypothesis Estimate Est.Error CI.Lower CI.Upper Evid.Ratio Post.Prob
## 1 (difficulty) < 0 0 0 0 0 56.42 0.98
## Star
## 1 *
## ---
## 'CI': 90%-CI for one-sided and 95%-CI for two-sided hypotheses.
## '*': For one-sided hypotheses, the posterior probability exceeds 95%;
## for two-sided hypotheses, the value tested against lies outside the 95%-CI.
## Posterior probabilities of point hypotheses assume equal prior probabilities.hypothesis(covariates_dist_mdl, 'self_contribution > 0')## Hypothesis Tests for class b:
## Hypothesis Estimate Est.Error CI.Lower CI.Upper Evid.Ratio
## 1 (self_contribution) > 0 0 0 0 0 1.9
## Post.Prob Star
## 1 0.66
## ---
## 'CI': 90%-CI for one-sided and 95%-CI for two-sided hypotheses.
## '*': For one-sided hypotheses, the posterior probability exceeds 95%;
## for two-sided hypotheses, the value tested against lies outside the 95%-CI.
## Posterior probabilities of point hypotheses assume equal prior probabilities.hypothesis(covariates_dist_mdl, 'other_contribution > 0')## Hypothesis Tests for class b:
## Hypothesis Estimate Est.Error CI.Lower CI.Upper Evid.Ratio
## 1 (other_contribution) > 0 0.01 0 0 0.01 Inf
## Post.Prob Star
## 1 1 *
## ---
## 'CI': 90%-CI for one-sided and 95%-CI for two-sided hypotheses.
## '*': For one-sided hypotheses, the posterior probability exceeds 95%;
## for two-sided hypotheses, the value tested against lies outside the 95%-CI.
## Posterior probabilities of point hypotheses assume equal prior probabilities.10 Difficulty analysis
As we are learning from the first experiment, this analysis already
directly includes difficulty as a covariate. We’ll test the effect of
difficulty on category anyway, and also on
subclusters!
Make a graph of this.
# Plot core:
category_difficulty_p <- df %>%
ggplot(aes(x = difficulty, fill = category)) +
geom_density(alpha = 0.55) +
annotate(geom = 'text',
label = 'concrete concepts',
color = 'goldenrod3',
x = 39, y = 0.011,
hjust = 0, size = 4) +
annotate(geom = 'text',
label = 'abstract concepts',
color = 'steelblue',
x = 68, y = 0.0075,
hjust = 0, size = 4)
# Scales and axes:
category_difficulty_p <- category_difficulty_p +
scale_x_continuous(expand = c(0, 0),
limits = c(0, 100),
breaks = seq(0, 100, 25)) +
scale_y_continuous(expand = c(0, 0),
limits = c(0, 0.02)) +
scale_fill_manual(values = c('goldenrod3', 'steelblue')) +
xlab('Difficulty') +
ylab('Density')
# Cosmetics:
category_difficulty_p <- category_difficulty_p +
theme_classic() +
theme(legend.position = 'none',
legend.title = element_blank(),
axis.title = element_text(face = 'bold',
size = 12.5),
axis.title.x = element_text(margin = margin(t = 6.5)),
axis.title.y = element_text(margin = margin(r = 10)))
# Show:
category_difficulty_p
ggsave('../figures_E2/category_difficulty_E2.pdf', plot = category_difficulty_p,
width = 5, height = 3.5)Since difficulty is now the dependent measure, convert
it into [0, 1] for beta regression. We’re adding 0.001 to
the zero cases here because otherwise we can’t run teh beta
regression.
df <- mutate(df,
difficulty_01 = difficulty / 100,
difficulty_01 = ifelse(difficulty_01 == 0, 0.001, difficulty_01))Model difficulty as a function of category
with a beta regression model then:
difficulty_mdl <- brm(bf(difficulty_01 ~
# Fixed effects:
1 +
category +
# Random effects:
(1 + category|participant) +
(1|word),
# Family-specific parameter (shape):
phi ~ 1 + category),
data = df, # interactive only
family = Beta,
# MCMC settings:
seed = 42,
init = 0,
cores = 4,
iter = 6000,
warmup = 3000,
control = list(adapt_delta = 0.99))
# Save model:
save(difficulty_mdl, file = '../models_E2/difficulty_mdl.Rdata')Load model:
load('../models_E2/difficulty_mdl.Rdata')Show priors:
prior_summary(difficulty_mdl)## prior class coef group resp dpar nlpar lb
## (flat) b
## (flat) b categoryabstract
## (flat) b phi
## (flat) b categoryabstract phi
## student_t(3, 0, 2.5) Intercept
## student_t(3, 0, 2.5) Intercept phi
## lkj_corr_cholesky(1) L
## lkj_corr_cholesky(1) L participant
## student_t(3, 0, 2.5) sd 0
## student_t(3, 0, 2.5) sd participant 0
## student_t(3, 0, 2.5) sd categoryabstract participant 0
## student_t(3, 0, 2.5) sd Intercept participant 0
## student_t(3, 0, 2.5) sd word 0
## student_t(3, 0, 2.5) sd Intercept word 0
## ub source
## default
## (vectorized)
## default
## (vectorized)
## default
## default
## default
## (vectorized)
## default
## (vectorized)
## (vectorized)
## (vectorized)
## (vectorized)
## (vectorized)Check posterior predictive checks of the mixed beta regression:
pp_check(difficulty_mdl, ndraws = 100)
Check this model:
difficulty_mdl## Family: beta
## Links: mu = logit; phi = log
## Formula: difficulty_01 ~ 1 + category + (1 + category | participant) + (1 | word)
## phi ~ 1 + category
## Data: df (Number of observations: 1032)
## Draws: 4 chains, each with iter = 6000; warmup = 3000; thin = 1;
## total post-warmup draws = 12000
##
## Group-Level Effects:
## ~participant (Number of levels: 129)
## Estimate Est.Error l-95% CI u-95% CI Rhat
## sd(Intercept) 0.80 0.07 0.67 0.95 1.00
## sd(categoryabstract) 0.64 0.09 0.46 0.81 1.00
## cor(Intercept,categoryabstract) -0.36 0.13 -0.59 -0.09 1.00
## Bulk_ESS Tail_ESS
## sd(Intercept) 4819 7275
## sd(categoryabstract) 2972 3568
## cor(Intercept,categoryabstract) 5526 7434
##
## ~word (Number of levels: 32)
## Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
## sd(Intercept) 0.07 0.05 0.00 0.17 1.00 3638 5474
##
## Population-Level Effects:
## Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS
## Intercept -0.91 0.08 -1.08 -0.74 1.00 4908
## phi_Intercept 1.45 0.07 1.32 1.59 1.00 8858
## categoryabstract 0.07 0.09 -0.11 0.24 1.00 8411
## phi_categoryabstract 0.01 0.10 -0.19 0.20 1.00 12204
## Tail_ESS
## Intercept 7000
## phi_Intercept 8930
## categoryabstract 9773
## phi_categoryabstract 9624
##
## Draws were sampled using sampling(NUTS). For each parameter, Bulk_ESS
## and Tail_ESS are effective sample size measures, and Rhat is the potential
## scale reduction factor on split chains (at convergence, Rhat = 1).Perform hypothesis test on the category fixed effects
coefficient:
hypothesis(difficulty_mdl, 'categoryabstract > 0')## Hypothesis Tests for class b:
## Hypothesis Estimate Est.Error CI.Lower CI.Upper Evid.Ratio
## 1 (categoryabstract) > 0 0.07 0.09 -0.08 0.21 3.71
## Post.Prob Star
## 1 0.79
## ---
## 'CI': 90%-CI for one-sided and 95%-CI for two-sided hypotheses.
## '*': For one-sided hypotheses, the posterior probability exceeds 95%;
## for two-sided hypotheses, the value tested against lies outside the 95%-CI.
## Posterior probabilities of point hypotheses assume equal prior probabilities.Model difficulty as a function of
subcluster with a beta regression model then:
diff_subcluster_mdl <- brm(bf(difficulty_01 ~
# Fixed effects:
1 +
subcluster +
# Random effects:
(1 + subcluster|participant) +
(1|word),
# Family-specific parameter (shape):
phi ~ 1),
data = df, # interactive only
family = Beta,
# MCMC settings:
seed = 42,
init = 0,
cores = 4,
iter = 6000,
warmup = 3000,
control = list(adapt_delta = 0.99))
# Save model:
save(diff_subcluster_mdl,
file = '../models_E2/difficulty_subcluster_mdl.Rdata')Load model:
load('../models_E2/difficulty_subcluster_mdl.Rdata')Show priors:
prior_summary(diff_subcluster_mdl)## prior class coef group resp dpar nlpar
## (flat) b
## (flat) b subclusterConc_an
## (flat) b subclusterConc_in
## (flat) b subclusterEM
## (flat) b subclusterPS
## (flat) b subclusterSS
## student_t(3, 0, 2.5) Intercept
## student_t(3, 0, 2.5) Intercept phi
## lkj_corr_cholesky(1) L
## lkj_corr_cholesky(1) L participant
## student_t(3, 0, 2.5) sd
## student_t(3, 0, 2.5) sd participant
## student_t(3, 0, 2.5) sd Intercept participant
## student_t(3, 0, 2.5) sd subclusterConc_an participant
## student_t(3, 0, 2.5) sd subclusterConc_in participant
## student_t(3, 0, 2.5) sd subclusterEM participant
## student_t(3, 0, 2.5) sd subclusterPS participant
## student_t(3, 0, 2.5) sd subclusterSS participant
## student_t(3, 0, 2.5) sd word
## student_t(3, 0, 2.5) sd Intercept word
## lb ub source
## default
## (vectorized)
## (vectorized)
## (vectorized)
## (vectorized)
## (vectorized)
## default
## default
## default
## (vectorized)
## 0 default
## 0 (vectorized)
## 0 (vectorized)
## 0 (vectorized)
## 0 (vectorized)
## 0 (vectorized)
## 0 (vectorized)
## 0 (vectorized)
## 0 (vectorized)
## 0 (vectorized)Check posterior predictive checks of the mixed beta regression:
pp_check(diff_subcluster_mdl, ndraws = 100)
Check this model:
diff_subcluster_mdl## Family: beta
## Links: mu = logit; phi = log
## Formula: difficulty_01 ~ 1 + subcluster + (1 + subcluster | participant) + (1 | word)
## phi ~ 1
## Data: df (Number of observations: 1032)
## Draws: 4 chains, each with iter = 6000; warmup = 3000; thin = 1;
## total post-warmup draws = 12000
##
## Group-Level Effects:
## ~participant (Number of levels: 129)
## Estimate Est.Error l-95% CI u-95% CI
## sd(Intercept) 0.80 0.08 0.66 0.96
## sd(subclusterConc_an) 0.63 0.12 0.40 0.87
## sd(subclusterConc_in) 0.57 0.12 0.33 0.80
## sd(subclusterEM) 0.13 0.09 0.01 0.34
## sd(subclusterPS) 0.38 0.20 0.03 0.74
## sd(subclusterSS) 0.23 0.16 0.01 0.59
## cor(Intercept,subclusterConc_an) -0.32 0.15 -0.58 -0.00
## cor(Intercept,subclusterConc_in) -0.27 0.17 -0.56 0.09
## cor(subclusterConc_an,subclusterConc_in) 0.84 0.10 0.58 0.97
## cor(Intercept,subclusterEM) -0.03 0.36 -0.68 0.67
## cor(subclusterConc_an,subclusterEM) 0.22 0.38 -0.59 0.83
## cor(subclusterConc_in,subclusterEM) 0.20 0.38 -0.58 0.81
## cor(Intercept,subclusterPS) 0.05 0.27 -0.47 0.61
## cor(subclusterConc_an,subclusterPS) -0.17 0.30 -0.73 0.45
## cor(subclusterConc_in,subclusterPS) -0.20 0.31 -0.76 0.43
## cor(subclusterEM,subclusterPS) 0.04 0.37 -0.67 0.72
## cor(Intercept,subclusterSS) 0.03 0.34 -0.62 0.67
## cor(subclusterConc_an,subclusterSS) -0.14 0.35 -0.75 0.59
## cor(subclusterConc_in,subclusterSS) -0.06 0.35 -0.70 0.63
## cor(subclusterEM,subclusterSS) 0.02 0.38 -0.70 0.71
## cor(subclusterPS,subclusterSS) -0.07 0.36 -0.73 0.66
## Rhat Bulk_ESS Tail_ESS
## sd(Intercept) 1.00 5613 8177
## sd(subclusterConc_an) 1.00 2519 2696
## sd(subclusterConc_in) 1.00 2462 2599
## sd(subclusterEM) 1.00 4782 6866
## sd(subclusterPS) 1.00 1859 3702
## sd(subclusterSS) 1.00 3083 5538
## cor(Intercept,subclusterConc_an) 1.00 6903 6238
## cor(Intercept,subclusterConc_in) 1.00 6896 6271
## cor(subclusterConc_an,subclusterConc_in) 1.00 4286 5245
## cor(Intercept,subclusterEM) 1.00 23371 9032
## cor(subclusterConc_an,subclusterEM) 1.00 9727 9454
## cor(subclusterConc_in,subclusterEM) 1.00 9104 9359
## cor(Intercept,subclusterPS) 1.00 13260 7111
## cor(subclusterConc_an,subclusterPS) 1.00 5943 8008
## cor(subclusterConc_in,subclusterPS) 1.00 6323 8785
## cor(subclusterEM,subclusterPS) 1.00 4300 7288
## cor(Intercept,subclusterSS) 1.00 19394 8511
## cor(subclusterConc_an,subclusterSS) 1.00 11677 9111
## cor(subclusterConc_in,subclusterSS) 1.00 12842 9681
## cor(subclusterEM,subclusterSS) 1.00 9320 10741
## cor(subclusterPS,subclusterSS) 1.00 9564 10460
##
## ~word (Number of levels: 32)
## Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
## sd(Intercept) 0.10 0.05 0.01 0.21 1.00 3198 5584
##
## Population-Level Effects:
## Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
## Intercept -0.89 0.12 -1.13 -0.65 1.00 7021 8360
## phi_Intercept 1.50 0.06 1.38 1.62 1.00 3583 6923
## subclusterConc_an -0.03 0.13 -0.29 0.24 1.00 9299 8963
## subclusterConc_in -0.04 0.13 -0.30 0.22 1.00 9631 9182
## subclusterEM 0.04 0.13 -0.22 0.30 1.00 10297 8970
## subclusterPS 0.11 0.14 -0.17 0.40 1.00 11618 10169
## subclusterSS -0.03 0.15 -0.33 0.27 1.00 12011 10029
##
## Draws were sampled using sampling(NUTS). For each parameter, Bulk_ESS
## and Tail_ESS are effective sample size measures, and Rhat is the potential
## scale reduction factor on split chains (at convergence, Rhat = 1).Perform hypothesis test on the subcluster fixed effects
coefficient:
# ...11 Category analysis: other-contribution
Do the main analysis of IOS with difficulty
as a covariate predictor, to control for this.
IOS_category_mdl <- brm(IOS ~
# Fixed effects:
1 +
category +
other_contribution_c +
difficulty_c +
category:other_contribution_c +
# Random effects:
(1 +
category +
other_contribution_c +
category:other_contribution_c|participant) +
(1 + other_contribution_c|word),
data = df,
family = cumulative,
# MCMC settings:
seed = 42,
cores = 4,
iter = 6000,
warmup = 3000,
save_pars = save_pars(all = TRUE), # for bayes factors
control = list(adapt_delta = 0.99))
# Save model:
save(IOS_category_mdl,
file = '../models_E2/IOS_category_mdl.Rdata')Corresponding null model:
IOS_category_null <- brm(IOS ~
# Fixed effects:
1 +
category +
other_contribution_c +
difficulty_c +
# Random effects:
(1 +
category +
other_contribution_c +
category:other_contribution_c|participant) +
(1 + other_contribution_c|word),
data = df,
family = cumulative,
# MCMC settings:
seed = 42,
cores = 4,
iter = 6000,
warmup = 3000,
save_pars = save_pars(all = TRUE), # for bayes factor
control = list(adapt_delta = 0.99))
# Save model:
save(IOS_category_null,
file = '../models_E2/IOS_category_null.Rdata')Load model:
load('../models_E2/IOS_category_mdl.Rdata')
load('../models_E2/IOS_category_null.Rdata')Show priors:
prior_summary(IOS_category_mdl)## prior class coef
## (flat) b
## (flat) b categoryabstract
## (flat) b categoryabstract:other_contribution_c
## (flat) b difficulty_c
## (flat) b other_contribution_c
## student_t(3, 0, 2.5) Intercept
## student_t(3, 0, 2.5) Intercept 1
## student_t(3, 0, 2.5) Intercept 2
## student_t(3, 0, 2.5) Intercept 3
## student_t(3, 0, 2.5) Intercept 4
## student_t(3, 0, 2.5) Intercept 5
## lkj_corr_cholesky(1) L
## lkj_corr_cholesky(1) L
## lkj_corr_cholesky(1) L
## student_t(3, 0, 2.5) sd
## student_t(3, 0, 2.5) sd
## student_t(3, 0, 2.5) sd categoryabstract
## student_t(3, 0, 2.5) sd categoryabstract:other_contribution_c
## student_t(3, 0, 2.5) sd Intercept
## student_t(3, 0, 2.5) sd other_contribution_c
## student_t(3, 0, 2.5) sd
## student_t(3, 0, 2.5) sd Intercept
## student_t(3, 0, 2.5) sd other_contribution_c
## group resp dpar nlpar lb ub source
## default
## (vectorized)
## (vectorized)
## (vectorized)
## (vectorized)
## default
## (vectorized)
## (vectorized)
## (vectorized)
## (vectorized)
## (vectorized)
## default
## participant (vectorized)
## word (vectorized)
## 0 default
## participant 0 (vectorized)
## participant 0 (vectorized)
## participant 0 (vectorized)
## participant 0 (vectorized)
## participant 0 (vectorized)
## word 0 (vectorized)
## word 0 (vectorized)
## word 0 (vectorized)prior_summary(IOS_category_null)## prior class coef
## (flat) b
## (flat) b categoryabstract
## (flat) b difficulty_c
## (flat) b other_contribution_c
## student_t(3, 0, 2.5) Intercept
## student_t(3, 0, 2.5) Intercept 1
## student_t(3, 0, 2.5) Intercept 2
## student_t(3, 0, 2.5) Intercept 3
## student_t(3, 0, 2.5) Intercept 4
## student_t(3, 0, 2.5) Intercept 5
## lkj_corr_cholesky(1) L
## lkj_corr_cholesky(1) L
## lkj_corr_cholesky(1) L
## student_t(3, 0, 2.5) sd
## student_t(3, 0, 2.5) sd
## student_t(3, 0, 2.5) sd categoryabstract
## student_t(3, 0, 2.5) sd categoryabstract:other_contribution_c
## student_t(3, 0, 2.5) sd Intercept
## student_t(3, 0, 2.5) sd other_contribution_c
## student_t(3, 0, 2.5) sd
## student_t(3, 0, 2.5) sd Intercept
## student_t(3, 0, 2.5) sd other_contribution_c
## group resp dpar nlpar lb ub source
## default
## (vectorized)
## (vectorized)
## (vectorized)
## default
## (vectorized)
## (vectorized)
## (vectorized)
## (vectorized)
## (vectorized)
## default
## participant (vectorized)
## word (vectorized)
## 0 default
## participant 0 (vectorized)
## participant 0 (vectorized)
## participant 0 (vectorized)
## participant 0 (vectorized)
## participant 0 (vectorized)
## word 0 (vectorized)
## word 0 (vectorized)
## word 0 (vectorized)Bayes factors for both:
# Compute:
IOS_bf <- bayes_factor(IOS_category_mdl, IOS_category_null)
# Save:
save(IOS_bf,
file = '../models_E2/IOS_bf.RData')Show Bayes factor:
# Load:
load('../models_E2/IOS_bf.RData')
# Show:
IOS_bf## Estimated Bayes factor in favor of IOS_category_mdl over IOS_category_null: 0.07764Compute R-squared:
bayes_R2(IOS_category_mdl)## Warning: Predictions are treated as continuous variables in 'bayes_R2' which is
## likely invalid for ordinal families.## Estimate Est.Error Q2.5 Q97.5
## R2 0.7081655 0.01295892 0.6811916 0.7317703bayes_R2(IOS_category_null)## Warning: Predictions are treated as continuous variables in 'bayes_R2' which is
## likely invalid for ordinal families.## Estimate Est.Error Q2.5 Q97.5
## R2 0.7086503 0.01252542 0.6828421 0.7315246# Check:
0.7081655 - 0.7086503## [1] -0.0004848The model with the interaction is nearly equivalent in R-squared to the model without the interaction.
Check posterior predictive checks of the mixed beta regression:
pp_check(IOS_category_mdl, ndraws = 100)
Check this model:
IOS_category_mdl## Family: cumulative
## Links: mu = logit; disc = identity
## Formula: IOS ~ 1 + category + other_contribution_c + difficulty_c + category:other_contribution_c + (1 + category + other_contribution_c + category:other_contribution_c | participant) + (1 + other_contribution_c | word)
## Data: df (Number of observations: 1032)
## Draws: 4 chains, each with iter = 6000; warmup = 3000; thin = 1;
## total post-warmup draws = 12000
##
## Group-Level Effects:
## ~participant (Number of levels: 129)
## Estimate
## sd(Intercept) 2.80
## sd(categoryabstract) 1.58
## sd(other_contribution_c) 0.06
## sd(categoryabstract:other_contribution_c) 0.06
## cor(Intercept,categoryabstract) -0.34
## cor(Intercept,other_contribution_c) 0.13
## cor(categoryabstract,other_contribution_c) 0.03
## cor(Intercept,categoryabstract:other_contribution_c) -0.11
## cor(categoryabstract,categoryabstract:other_contribution_c) -0.03
## cor(other_contribution_c,categoryabstract:other_contribution_c) -0.54
## Est.Error
## sd(Intercept) 0.25
## sd(categoryabstract) 0.29
## sd(other_contribution_c) 0.01
## sd(categoryabstract:other_contribution_c) 0.02
## cor(Intercept,categoryabstract) 0.14
## cor(Intercept,other_contribution_c) 0.16
## cor(categoryabstract,other_contribution_c) 0.22
## cor(Intercept,categoryabstract:other_contribution_c) 0.20
## cor(categoryabstract,categoryabstract:other_contribution_c) 0.26
## cor(other_contribution_c,categoryabstract:other_contribution_c) 0.27
## l-95% CI
## sd(Intercept) 2.33
## sd(categoryabstract) 1.00
## sd(other_contribution_c) 0.04
## sd(categoryabstract:other_contribution_c) 0.01
## cor(Intercept,categoryabstract) -0.57
## cor(Intercept,other_contribution_c) -0.19
## cor(categoryabstract,other_contribution_c) -0.40
## cor(Intercept,categoryabstract:other_contribution_c) -0.52
## cor(categoryabstract,categoryabstract:other_contribution_c) -0.48
## cor(other_contribution_c,categoryabstract:other_contribution_c) -0.86
## u-95% CI Rhat
## sd(Intercept) 3.33 1.00
## sd(categoryabstract) 2.14 1.00
## sd(other_contribution_c) 0.09 1.01
## sd(categoryabstract:other_contribution_c) 0.10 1.01
## cor(Intercept,categoryabstract) -0.05 1.00
## cor(Intercept,other_contribution_c) 0.43 1.00
## cor(categoryabstract,other_contribution_c) 0.45 1.01
## cor(Intercept,categoryabstract:other_contribution_c) 0.27 1.00
## cor(categoryabstract,categoryabstract:other_contribution_c) 0.56 1.00
## cor(other_contribution_c,categoryabstract:other_contribution_c) 0.22 1.00
## Bulk_ESS
## sd(Intercept) 2547
## sd(categoryabstract) 1101
## sd(other_contribution_c) 805
## sd(categoryabstract:other_contribution_c) 435
## cor(Intercept,categoryabstract) 3174
## cor(Intercept,other_contribution_c) 5028
## cor(categoryabstract,other_contribution_c) 1367
## cor(Intercept,categoryabstract:other_contribution_c) 5323
## cor(categoryabstract,categoryabstract:other_contribution_c) 1432
## cor(other_contribution_c,categoryabstract:other_contribution_c) 866
## Tail_ESS
## sd(Intercept) 5018
## sd(categoryabstract) 1369
## sd(other_contribution_c) 2128
## sd(categoryabstract:other_contribution_c) 597
## cor(Intercept,categoryabstract) 3755
## cor(Intercept,other_contribution_c) 6635
## cor(categoryabstract,other_contribution_c) 2430
## cor(Intercept,categoryabstract:other_contribution_c) 2966
## cor(categoryabstract,categoryabstract:other_contribution_c) 1471
## cor(other_contribution_c,categoryabstract:other_contribution_c) 971
##
## ~word (Number of levels: 32)
## Estimate Est.Error l-95% CI u-95% CI Rhat
## sd(Intercept) 0.09 0.07 0.00 0.26 1.00
## sd(other_contribution_c) 0.01 0.01 0.00 0.02 1.00
## cor(Intercept,other_contribution_c) 0.01 0.58 -0.95 0.96 1.00
## Bulk_ESS Tail_ESS
## sd(Intercept) 6987 5823
## sd(other_contribution_c) 4197 5680
## cor(Intercept,other_contribution_c) 6166 7073
##
## Population-Level Effects:
## Estimate Est.Error l-95% CI u-95% CI Rhat
## Intercept[1] -5.60 0.37 -6.32 -4.90 1.00
## Intercept[2] -1.86 0.29 -2.44 -1.29 1.00
## Intercept[3] 0.93 0.29 0.37 1.50 1.00
## Intercept[4] 3.26 0.32 2.65 3.89 1.00
## Intercept[5] 5.96 0.39 5.21 6.75 1.00
## categoryabstract 0.02 0.22 -0.40 0.45 1.00
## other_contribution_c 0.06 0.01 0.04 0.08 1.00
## difficulty_c -0.03 0.00 -0.04 -0.02 1.00
## categoryabstract:other_contribution_c 0.00 0.01 -0.02 0.03 1.00
## Bulk_ESS Tail_ESS
## Intercept[1] 3186 6206
## Intercept[2] 2808 5001
## Intercept[3] 2817 4706
## Intercept[4] 3047 5276
## Intercept[5] 3284 6077
## categoryabstract 6039 8332
## other_contribution_c 3773 6786
## difficulty_c 10301 9445
## categoryabstract:other_contribution_c 6117 7567
##
## Family Specific Parameters:
## Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
## disc 1.00 0.00 1.00 1.00 NA NA NA
##
## Draws were sampled using sampling(NUTS). For each parameter, Bulk_ESS
## and Tail_ESS are effective sample size measures, and Rhat is the potential
## scale reduction factor on split chains (at convergence, Rhat = 1).Perform hypothesis tests on the fixed effects coefficient:
hypothesis(IOS_category_mdl,
'categoryabstract < 0')## Hypothesis Tests for class b:
## Hypothesis Estimate Est.Error CI.Lower CI.Upper Evid.Ratio
## 1 (categoryabstract) < 0 0.02 0.22 -0.33 0.38 0.83
## Post.Prob Star
## 1 0.45
## ---
## 'CI': 90%-CI for one-sided and 95%-CI for two-sided hypotheses.
## '*': For one-sided hypotheses, the posterior probability exceeds 95%;
## for two-sided hypotheses, the value tested against lies outside the 95%-CI.
## Posterior probabilities of point hypotheses assume equal prior probabilities.hypothesis(IOS_category_mdl,
'difficulty_c < 0')## Hypothesis Tests for class b:
## Hypothesis Estimate Est.Error CI.Lower CI.Upper Evid.Ratio Post.Prob
## 1 (difficulty_c) < 0 -0.03 0 -0.04 -0.03 Inf 1
## Star
## 1 *
## ---
## 'CI': 90%-CI for one-sided and 95%-CI for two-sided hypotheses.
## '*': For one-sided hypotheses, the posterior probability exceeds 95%;
## for two-sided hypotheses, the value tested against lies outside the 95%-CI.
## Posterior probabilities of point hypotheses assume equal prior probabilities.hypothesis(IOS_category_mdl,
'other_contribution_c > 0')## Hypothesis Tests for class b:
## Hypothesis Estimate Est.Error CI.Lower CI.Upper Evid.Ratio
## 1 (other_contributi... > 0 0.06 0.01 0.04 0.08 Inf
## Post.Prob Star
## 1 1 *
## ---
## 'CI': 90%-CI for one-sided and 95%-CI for two-sided hypotheses.
## '*': For one-sided hypotheses, the posterior probability exceeds 95%;
## for two-sided hypotheses, the value tested against lies outside the 95%-CI.
## Posterior probabilities of point hypotheses assume equal prior probabilities.hypothesis(IOS_category_mdl,
'categoryabstract:other_contribution_c > 0')## Hypothesis Tests for class b:
## Hypothesis Estimate Est.Error CI.Lower CI.Upper Evid.Ratio
## 1 (categoryabstract... > 0 0 0.01 -0.02 0.02 1.73
## Post.Prob Star
## 1 0.63
## ---
## 'CI': 90%-CI for one-sided and 95%-CI for two-sided hypotheses.
## '*': For one-sided hypotheses, the posterior probability exceeds 95%;
## for two-sided hypotheses, the value tested against lies outside the 95%-CI.
## Posterior probabilities of point hypotheses assume equal prior probabilities.Re-do the other main model, the one with closeness_01 as
dependent variable, this time also with a difficulty_c
control covariate:
dist_mdl <- brm(bf(closeness_01 ~
# Fixed effects:
1 +
category +
other_contribution_c +
difficulty_c +
category:other_contribution_c +
# Random effects:
(1 +
category +
other_contribution_c +
category:other_contribution_c|participant) +
(1 + other_contribution_c|word),
phi ~ 1 + category),
data = df, # interactive only
family = Beta,
# MCMC settings:
seed = 42,
init = 0,
cores = 4,
iter = 7500,
warmup = 3500,
save_pars = save_pars(all = TRUE), # for bayes factor
control = list(adapt_delta = 0.99))
# Save model:
save(dist_mdl,
file = '../models_E2/dist_mdl.Rdata')Corresponding null model:
dist_null_mdl <- brm(bf(closeness_01 ~
# Fixed effects:
1 +
category +
other_contribution_c +
difficulty_c +
# Random effects:
(1 +
category +
other_contribution_c +
category:other_contribution_c|participant) +
(1 + other_contribution_c|word),
phi ~ 1 + category),
data = df, # interactive only
family = Beta,
# MCMC settings:
seed = 42,
init = 0,
cores = 4,
iter = 7500,
warmup = 3500,
save_pars = save_pars(all = TRUE), # for bayes factor
control = list(adapt_delta = 0.99))
# Save model:
save(dist_null_mdl,
file = '../models_E2/dist_null_mdl.Rdata')Load model:
load('../models_E2/dist_mdl.Rdata')
load('../models_E2/dist_null_mdl.Rdata')Show priors:
prior_summary(dist_mdl)## prior class coef
## (flat) b
## (flat) b categoryabstract
## (flat) b categoryabstract:other_contribution_c
## (flat) b difficulty_c
## (flat) b other_contribution_c
## (flat) b
## (flat) b categoryabstract
## student_t(3, 0, 2.5) Intercept
## student_t(3, 0, 2.5) Intercept
## lkj_corr_cholesky(1) L
## lkj_corr_cholesky(1) L
## lkj_corr_cholesky(1) L
## student_t(3, 0, 2.5) sd
## student_t(3, 0, 2.5) sd
## student_t(3, 0, 2.5) sd categoryabstract
## student_t(3, 0, 2.5) sd categoryabstract:other_contribution_c
## student_t(3, 0, 2.5) sd Intercept
## student_t(3, 0, 2.5) sd other_contribution_c
## student_t(3, 0, 2.5) sd
## student_t(3, 0, 2.5) sd Intercept
## student_t(3, 0, 2.5) sd other_contribution_c
## group resp dpar nlpar lb ub source
## default
## (vectorized)
## (vectorized)
## (vectorized)
## (vectorized)
## phi default
## phi (vectorized)
## default
## phi default
## default
## participant (vectorized)
## word (vectorized)
## 0 default
## participant 0 (vectorized)
## participant 0 (vectorized)
## participant 0 (vectorized)
## participant 0 (vectorized)
## participant 0 (vectorized)
## word 0 (vectorized)
## word 0 (vectorized)
## word 0 (vectorized)prior_summary(dist_null_mdl)## prior class coef
## (flat) b
## (flat) b categoryabstract
## (flat) b difficulty_c
## (flat) b other_contribution_c
## (flat) b
## (flat) b categoryabstract
## student_t(3, 0, 2.5) Intercept
## student_t(3, 0, 2.5) Intercept
## lkj_corr_cholesky(1) L
## lkj_corr_cholesky(1) L
## lkj_corr_cholesky(1) L
## student_t(3, 0, 2.5) sd
## student_t(3, 0, 2.5) sd
## student_t(3, 0, 2.5) sd categoryabstract
## student_t(3, 0, 2.5) sd categoryabstract:other_contribution_c
## student_t(3, 0, 2.5) sd Intercept
## student_t(3, 0, 2.5) sd other_contribution_c
## student_t(3, 0, 2.5) sd
## student_t(3, 0, 2.5) sd Intercept
## student_t(3, 0, 2.5) sd other_contribution_c
## group resp dpar nlpar lb ub source
## default
## (vectorized)
## (vectorized)
## (vectorized)
## phi default
## phi (vectorized)
## default
## phi default
## default
## participant (vectorized)
## word (vectorized)
## 0 default
## participant 0 (vectorized)
## participant 0 (vectorized)
## participant 0 (vectorized)
## participant 0 (vectorized)
## participant 0 (vectorized)
## word 0 (vectorized)
## word 0 (vectorized)
## word 0 (vectorized)Bayes factors for both:
# Compute:
dist_bf <- bayes_factor(dist_mdl, dist_null_mdl)
# Save:
save(dist_bf,
file = '../models_E2/dist_bf.RData')Show Bayes factor:
# Load:
load('../models_E2/dist_bf.RData')
# Show:
dist_bf## Estimated Bayes factor in favor of dist_mdl over dist_null_mdl: 0.17835Check posterior predictive checks of the mixed beta regression:
pp_check(dist_mdl, ndraws = 100)
Check this model:
dist_mdl## Family: beta
## Links: mu = logit; phi = log
## Formula: closeness_01 ~ 1 + category + other_contribution_c + difficulty_c + category:other_contribution_c + (1 + category + other_contribution_c + category:other_contribution_c | participant) + (1 + other_contribution_c | word)
## phi ~ 1 + category
## Data: df (Number of observations: 1032)
## Draws: 4 chains, each with iter = 7500; warmup = 3500; thin = 1;
## total post-warmup draws = 16000
##
## Group-Level Effects:
## ~participant (Number of levels: 129)
## Estimate
## sd(Intercept) 0.91
## sd(categoryabstract) 0.50
## sd(other_contribution_c) 0.02
## sd(categoryabstract:other_contribution_c) 0.02
## cor(Intercept,categoryabstract) -0.39
## cor(Intercept,other_contribution_c) 0.08
## cor(categoryabstract,other_contribution_c) -0.20
## cor(Intercept,categoryabstract:other_contribution_c) -0.05
## cor(categoryabstract,categoryabstract:other_contribution_c) -0.11
## cor(other_contribution_c,categoryabstract:other_contribution_c) -0.13
## Est.Error
## sd(Intercept) 0.06
## sd(categoryabstract) 0.09
## sd(other_contribution_c) 0.00
## sd(categoryabstract:other_contribution_c) 0.00
## cor(Intercept,categoryabstract) 0.11
## cor(Intercept,other_contribution_c) 0.14
## cor(categoryabstract,other_contribution_c) 0.19
## cor(Intercept,categoryabstract:other_contribution_c) 0.16
## cor(categoryabstract,categoryabstract:other_contribution_c) 0.18
## cor(other_contribution_c,categoryabstract:other_contribution_c) 0.27
## l-95% CI
## sd(Intercept) 0.79
## sd(categoryabstract) 0.31
## sd(other_contribution_c) 0.01
## sd(categoryabstract:other_contribution_c) 0.01
## cor(Intercept,categoryabstract) -0.59
## cor(Intercept,other_contribution_c) -0.20
## cor(categoryabstract,other_contribution_c) -0.55
## cor(Intercept,categoryabstract:other_contribution_c) -0.37
## cor(categoryabstract,categoryabstract:other_contribution_c) -0.45
## cor(other_contribution_c,categoryabstract:other_contribution_c) -0.57
## u-95% CI Rhat
## sd(Intercept) 1.05 1.00
## sd(categoryabstract) 0.68 1.00
## sd(other_contribution_c) 0.02 1.00
## sd(categoryabstract:other_contribution_c) 0.03 1.00
## cor(Intercept,categoryabstract) -0.15 1.00
## cor(Intercept,other_contribution_c) 0.37 1.00
## cor(categoryabstract,other_contribution_c) 0.19 1.00
## cor(Intercept,categoryabstract:other_contribution_c) 0.26 1.00
## cor(categoryabstract,categoryabstract:other_contribution_c) 0.25 1.00
## cor(other_contribution_c,categoryabstract:other_contribution_c) 0.48 1.00
## Bulk_ESS
## sd(Intercept) 3907
## sd(categoryabstract) 1584
## sd(other_contribution_c) 2687
## sd(categoryabstract:other_contribution_c) 1702
## cor(Intercept,categoryabstract) 7223
## cor(Intercept,other_contribution_c) 7786
## cor(categoryabstract,other_contribution_c) 2170
## cor(Intercept,categoryabstract:other_contribution_c) 9692
## cor(categoryabstract,categoryabstract:other_contribution_c) 5147
## cor(other_contribution_c,categoryabstract:other_contribution_c) 1510
## Tail_ESS
## sd(Intercept) 6903
## sd(categoryabstract) 2092
## sd(other_contribution_c) 5945
## sd(categoryabstract:other_contribution_c) 2945
## cor(Intercept,categoryabstract) 9980
## cor(Intercept,other_contribution_c) 10675
## cor(categoryabstract,other_contribution_c) 3359
## cor(Intercept,categoryabstract:other_contribution_c) 10497
## cor(categoryabstract,categoryabstract:other_contribution_c) 8205
## cor(other_contribution_c,categoryabstract:other_contribution_c) 2791
##
## ~word (Number of levels: 32)
## Estimate Est.Error l-95% CI u-95% CI Rhat
## sd(Intercept) 0.04 0.03 0.00 0.10 1.00
## sd(other_contribution_c) 0.00 0.00 0.00 0.00 1.00
## cor(Intercept,other_contribution_c) 0.00 0.56 -0.94 0.94 1.00
## Bulk_ESS Tail_ESS
## sd(Intercept) 4513 6859
## sd(other_contribution_c) 5232 7474
## cor(Intercept,other_contribution_c) 10453 10039
##
## Population-Level Effects:
## Estimate Est.Error l-95% CI u-95% CI Rhat
## Intercept 0.95 0.09 0.78 1.12 1.00
## phi_Intercept 3.58 0.08 3.42 3.73 1.00
## categoryabstract -0.03 0.06 -0.15 0.10 1.00
## other_contribution_c 0.02 0.00 0.01 0.02 1.00
## difficulty_c -0.01 0.00 -0.01 -0.00 1.00
## categoryabstract:other_contribution_c -0.00 0.00 -0.01 0.00 1.00
## phi_categoryabstract -0.33 0.13 -0.58 -0.08 1.00
## Bulk_ESS Tail_ESS
## Intercept 2311 4677
## phi_Intercept 11617 12038
## categoryabstract 8504 10700
## other_contribution_c 9558 10827
## difficulty_c 18767 14975
## categoryabstract:other_contribution_c 11433 12172
## phi_categoryabstract 5046 9603
##
## Draws were sampled using sampling(NUTS). For each parameter, Bulk_ESS
## and Tail_ESS are effective sample size measures, and Rhat is the potential
## scale reduction factor on split chains (at convergence, Rhat = 1).Perform hypothesis tests on the fixed effects coefficient:
hypothesis(dist_mdl,
'categoryabstract > 0')## Hypothesis Tests for class b:
## Hypothesis Estimate Est.Error CI.Lower CI.Upper Evid.Ratio
## 1 (categoryabstract) > 0 -0.03 0.06 -0.13 0.08 0.5
## Post.Prob Star
## 1 0.33
## ---
## 'CI': 90%-CI for one-sided and 95%-CI for two-sided hypotheses.
## '*': For one-sided hypotheses, the posterior probability exceeds 95%;
## for two-sided hypotheses, the value tested against lies outside the 95%-CI.
## Posterior probabilities of point hypotheses assume equal prior probabilities.hypothesis(dist_mdl,
'difficulty_c < 0')## Hypothesis Tests for class b:
## Hypothesis Estimate Est.Error CI.Lower CI.Upper Evid.Ratio Post.Prob
## 1 (difficulty_c) < 0 -0.01 0 -0.01 0 Inf 1
## Star
## 1 *
## ---
## 'CI': 90%-CI for one-sided and 95%-CI for two-sided hypotheses.
## '*': For one-sided hypotheses, the posterior probability exceeds 95%;
## for two-sided hypotheses, the value tested against lies outside the 95%-CI.
## Posterior probabilities of point hypotheses assume equal prior probabilities.hypothesis(dist_mdl,
'other_contribution_c > 0')## Hypothesis Tests for class b:
## Hypothesis Estimate Est.Error CI.Lower CI.Upper Evid.Ratio
## 1 (other_contributi... > 0 0.02 0 0.01 0.02 Inf
## Post.Prob Star
## 1 1 *
## ---
## 'CI': 90%-CI for one-sided and 95%-CI for two-sided hypotheses.
## '*': For one-sided hypotheses, the posterior probability exceeds 95%;
## for two-sided hypotheses, the value tested against lies outside the 95%-CI.
## Posterior probabilities of point hypotheses assume equal prior probabilities.hypothesis(dist_mdl,
'categoryabstract:other_contribution_c > 0')## Hypothesis Tests for class b:
## Hypothesis Estimate Est.Error CI.Lower CI.Upper Evid.Ratio
## 1 (categoryabstract... > 0 0 0 -0.01 0 0.45
## Post.Prob Star
## 1 0.31
## ---
## 'CI': 90%-CI for one-sided and 95%-CI for two-sided hypotheses.
## '*': For one-sided hypotheses, the posterior probability exceeds 95%;
## for two-sided hypotheses, the value tested against lies outside the 95%-CI.
## Posterior probabilities of point hypotheses assume equal prior probabilities.12 Category analysis: self-contribution
A repeat of the main analysis, but this time testing the interaction
with other_contribution rather than
self_contribution.
IOS_self_mdl <- brm(IOS ~
# Fixed effects:
1 +
category +
self_contribution_c +
difficulty_c +
category:self_contribution_c +
# Random effects:
(1 +
category +
self_contribution_c +
category:self_contribution_c|participant) +
(1 + self_contribution_c|word),
data = df,
family = cumulative,
# MCMC settings:
seed = 42,
cores = 4,
iter = 6000,
warmup = 3000,
save_pars = save_pars(all = TRUE), # for bayes factors
control = list(adapt_delta = 0.99))
# Save model:
save(IOS_self_mdl,
file = '../models_E2/IOS_self_mdl.Rdata')Fit the corresponding null model:
IOS_self_null <- brm(IOS ~
# Fixed effects:
1 +
category +
self_contribution_c +
difficulty_c +
# Random effects:
(1 +
category +
self_contribution_c +
category:self_contribution_c|participant) +
(1 + self_contribution_c|word),
data = df,
family = cumulative,
# MCMC settings:
seed = 42,
cores = 4,
iter = 6000,
warmup = 3000,
save_pars = save_pars(all = TRUE), # for bayes factors
control = list(adapt_delta = 0.99))
# Save model:
save(IOS_null_mdl,
file = '../models_E2/IOS_self_null.Rdata')Load model:
load('../models_E2/IOS_self_mdl.RData')
load('../models_E2/IOS_self_null.RData')Show priors:
prior_summary(IOS_self_mdl)## prior class coef
## (flat) b
## (flat) b categoryabstract
## (flat) b categoryabstract:self_contribution_c
## (flat) b difficulty_c
## (flat) b self_contribution_c
## student_t(3, 0, 2.5) Intercept
## student_t(3, 0, 2.5) Intercept 1
## student_t(3, 0, 2.5) Intercept 2
## student_t(3, 0, 2.5) Intercept 3
## student_t(3, 0, 2.5) Intercept 4
## student_t(3, 0, 2.5) Intercept 5
## lkj_corr_cholesky(1) L
## lkj_corr_cholesky(1) L
## lkj_corr_cholesky(1) L
## student_t(3, 0, 2.5) sd
## student_t(3, 0, 2.5) sd
## student_t(3, 0, 2.5) sd categoryabstract
## student_t(3, 0, 2.5) sd categoryabstract:self_contribution_c
## student_t(3, 0, 2.5) sd Intercept
## student_t(3, 0, 2.5) sd self_contribution_c
## student_t(3, 0, 2.5) sd
## student_t(3, 0, 2.5) sd Intercept
## student_t(3, 0, 2.5) sd self_contribution_c
## group resp dpar nlpar lb ub source
## default
## (vectorized)
## (vectorized)
## (vectorized)
## (vectorized)
## default
## (vectorized)
## (vectorized)
## (vectorized)
## (vectorized)
## (vectorized)
## default
## participant (vectorized)
## word (vectorized)
## 0 default
## participant 0 (vectorized)
## participant 0 (vectorized)
## participant 0 (vectorized)
## participant 0 (vectorized)
## participant 0 (vectorized)
## word 0 (vectorized)
## word 0 (vectorized)
## word 0 (vectorized)prior_summary(IOS_self_null)## prior class coef
## (flat) b
## (flat) b categoryabstract
## (flat) b difficulty_c
## (flat) b self_contribution_c
## student_t(3, 0, 2.5) Intercept
## student_t(3, 0, 2.5) Intercept 1
## student_t(3, 0, 2.5) Intercept 2
## student_t(3, 0, 2.5) Intercept 3
## student_t(3, 0, 2.5) Intercept 4
## student_t(3, 0, 2.5) Intercept 5
## lkj_corr_cholesky(1) L
## lkj_corr_cholesky(1) L
## lkj_corr_cholesky(1) L
## student_t(3, 0, 2.5) sd
## student_t(3, 0, 2.5) sd
## student_t(3, 0, 2.5) sd categoryabstract
## student_t(3, 0, 2.5) sd categoryabstract:self_contribution_c
## student_t(3, 0, 2.5) sd Intercept
## student_t(3, 0, 2.5) sd self_contribution_c
## student_t(3, 0, 2.5) sd
## student_t(3, 0, 2.5) sd Intercept
## student_t(3, 0, 2.5) sd self_contribution_c
## group resp dpar nlpar lb ub source
## default
## (vectorized)
## (vectorized)
## (vectorized)
## default
## (vectorized)
## (vectorized)
## (vectorized)
## (vectorized)
## (vectorized)
## default
## participant (vectorized)
## word (vectorized)
## 0 default
## participant 0 (vectorized)
## participant 0 (vectorized)
## participant 0 (vectorized)
## participant 0 (vectorized)
## participant 0 (vectorized)
## word 0 (vectorized)
## word 0 (vectorized)
## word 0 (vectorized)Bayes factors for both:
# Compute:
IOS_self_bf <- bayes_factor(IOS_self_mdl, IOS_self_null)
# Save:
save(IOS_self_bf,
file = '../models_E2/IOS_self_bf.RData')Show Bayes factor:
# Load:
load('../models_E2/IOS_self_bf.RData')
# Show:
dist_bf## Estimated Bayes factor in favor of dist_mdl over dist_null_mdl: 0.17835Check posterior predictive checks of the mixed beta regression:
pp_check(IOS_self_mdl, ndraws = 100)
Check this model:
IOS_self_mdl## Family: cumulative
## Links: mu = logit; disc = identity
## Formula: IOS ~ 1 + category + self_contribution_c + difficulty_c + category:self_contribution_c + (1 + category + self_contribution_c + category:self_contribution_c | participant) + (1 + self_contribution_c | word)
## Data: df (Number of observations: 1032)
## Draws: 4 chains, each with iter = 6000; warmup = 3000; thin = 1;
## total post-warmup draws = 12000
##
## Group-Level Effects:
## ~participant (Number of levels: 129)
## Estimate
## sd(Intercept) 2.83
## sd(categoryabstract) 1.86
## sd(self_contribution_c) 0.06
## sd(categoryabstract:self_contribution_c) 0.03
## cor(Intercept,categoryabstract) -0.36
## cor(Intercept,self_contribution_c) 0.20
## cor(categoryabstract,self_contribution_c) 0.21
## cor(Intercept,categoryabstract:self_contribution_c) -0.33
## cor(categoryabstract,categoryabstract:self_contribution_c) 0.25
## cor(self_contribution_c,categoryabstract:self_contribution_c) -0.36
## Est.Error
## sd(Intercept) 0.25
## sd(categoryabstract) 0.24
## sd(self_contribution_c) 0.01
## sd(categoryabstract:self_contribution_c) 0.02
## cor(Intercept,categoryabstract) 0.11
## cor(Intercept,self_contribution_c) 0.17
## cor(categoryabstract,self_contribution_c) 0.20
## cor(Intercept,categoryabstract:self_contribution_c) 0.32
## cor(categoryabstract,categoryabstract:self_contribution_c) 0.31
## cor(self_contribution_c,categoryabstract:self_contribution_c) 0.39
## l-95% CI u-95% CI
## sd(Intercept) 2.37 3.36
## sd(categoryabstract) 1.38 2.35
## sd(self_contribution_c) 0.03 0.09
## sd(categoryabstract:self_contribution_c) 0.00 0.07
## cor(Intercept,categoryabstract) -0.56 -0.12
## cor(Intercept,self_contribution_c) -0.15 0.53
## cor(categoryabstract,self_contribution_c) -0.19 0.60
## cor(Intercept,categoryabstract:self_contribution_c) -0.86 0.40
## cor(categoryabstract,categoryabstract:self_contribution_c) -0.44 0.80
## cor(self_contribution_c,categoryabstract:self_contribution_c) -0.88 0.57
## Rhat Bulk_ESS
## sd(Intercept) 1.00 3480
## sd(categoryabstract) 1.00 2484
## sd(self_contribution_c) 1.00 1495
## sd(categoryabstract:self_contribution_c) 1.00 953
## cor(Intercept,categoryabstract) 1.00 3640
## cor(Intercept,self_contribution_c) 1.00 5636
## cor(categoryabstract,self_contribution_c) 1.00 3001
## cor(Intercept,categoryabstract:self_contribution_c) 1.00 6886
## cor(categoryabstract,categoryabstract:self_contribution_c) 1.00 7058
## cor(self_contribution_c,categoryabstract:self_contribution_c) 1.00 1680
## Tail_ESS
## sd(Intercept) 5591
## sd(categoryabstract) 3630
## sd(self_contribution_c) 3352
## sd(categoryabstract:self_contribution_c) 2509
## cor(Intercept,categoryabstract) 5889
## cor(Intercept,self_contribution_c) 7059
## cor(categoryabstract,self_contribution_c) 4470
## cor(Intercept,categoryabstract:self_contribution_c) 5555
## cor(categoryabstract,categoryabstract:self_contribution_c) 6983
## cor(self_contribution_c,categoryabstract:self_contribution_c) 6376
##
## ~word (Number of levels: 32)
## Estimate Est.Error l-95% CI u-95% CI Rhat
## sd(Intercept) 0.10 0.08 0.00 0.28 1.00
## sd(self_contribution_c) 0.01 0.01 0.00 0.02 1.00
## cor(Intercept,self_contribution_c) 0.17 0.57 -0.92 0.97 1.00
## Bulk_ESS Tail_ESS
## sd(Intercept) 5812 5571
## sd(self_contribution_c) 4054 6726
## cor(Intercept,self_contribution_c) 6091 7771
##
## Population-Level Effects:
## Estimate Est.Error l-95% CI u-95% CI Rhat
## Intercept[1] -5.47 0.36 -6.18 -4.78 1.00
## Intercept[2] -1.86 0.29 -2.44 -1.29 1.00
## Intercept[3] 0.86 0.29 0.31 1.43 1.00
## Intercept[4] 3.13 0.31 2.54 3.76 1.00
## Intercept[5] 5.76 0.38 5.04 6.54 1.00
## categoryabstract -0.03 0.22 -0.46 0.40 1.00
## self_contribution_c 0.05 0.01 0.03 0.07 1.00
## difficulty_c -0.03 0.00 -0.04 -0.02 1.00
## categoryabstract:self_contribution_c 0.00 0.01 -0.02 0.03 1.00
## Bulk_ESS Tail_ESS
## Intercept[1] 3763 6919
## Intercept[2] 3101 5445
## Intercept[3] 3125 5443
## Intercept[4] 3376 5949
## Intercept[5] 4277 7263
## categoryabstract 6368 8190
## self_contribution_c 5850 7587
## difficulty_c 12522 9687
## categoryabstract:self_contribution_c 7247 8878
##
## Family Specific Parameters:
## Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
## disc 1.00 0.00 1.00 1.00 NA NA NA
##
## Draws were sampled using sampling(NUTS). For each parameter, Bulk_ESS
## and Tail_ESS are effective sample size measures, and Rhat is the potential
## scale reduction factor on split chains (at convergence, Rhat = 1).Perform hypothesis tests on the fixed effects coefficient:
hypothesis(IOS_self_mdl,
'categoryabstract < 0')## Hypothesis Tests for class b:
## Hypothesis Estimate Est.Error CI.Lower CI.Upper Evid.Ratio
## 1 (categoryabstract) < 0 -0.03 0.22 -0.38 0.33 1.2
## Post.Prob Star
## 1 0.55
## ---
## 'CI': 90%-CI for one-sided and 95%-CI for two-sided hypotheses.
## '*': For one-sided hypotheses, the posterior probability exceeds 95%;
## for two-sided hypotheses, the value tested against lies outside the 95%-CI.
## Posterior probabilities of point hypotheses assume equal prior probabilities.hypothesis(IOS_self_mdl,
'difficulty_c < 0')## Hypothesis Tests for class b:
## Hypothesis Estimate Est.Error CI.Lower CI.Upper Evid.Ratio Post.Prob
## 1 (difficulty_c) < 0 -0.03 0 -0.04 -0.03 Inf 1
## Star
## 1 *
## ---
## 'CI': 90%-CI for one-sided and 95%-CI for two-sided hypotheses.
## '*': For one-sided hypotheses, the posterior probability exceeds 95%;
## for two-sided hypotheses, the value tested against lies outside the 95%-CI.
## Posterior probabilities of point hypotheses assume equal prior probabilities.hypothesis(IOS_self_mdl,
'self_contribution_c > 0')## Hypothesis Tests for class b:
## Hypothesis Estimate Est.Error CI.Lower CI.Upper Evid.Ratio
## 1 (self_contributio... > 0 0.05 0.01 0.03 0.07 Inf
## Post.Prob Star
## 1 1 *
## ---
## 'CI': 90%-CI for one-sided and 95%-CI for two-sided hypotheses.
## '*': For one-sided hypotheses, the posterior probability exceeds 95%;
## for two-sided hypotheses, the value tested against lies outside the 95%-CI.
## Posterior probabilities of point hypotheses assume equal prior probabilities.hypothesis(IOS_self_mdl,
'categoryabstract:self_contribution_c > 0')## Hypothesis Tests for class b:
## Hypothesis Estimate Est.Error CI.Lower CI.Upper Evid.Ratio
## 1 (categoryabstract... > 0 0 0.01 -0.02 0.02 1.57
## Post.Prob Star
## 1 0.61
## ---
## 'CI': 90%-CI for one-sided and 95%-CI for two-sided hypotheses.
## '*': For one-sided hypotheses, the posterior probability exceeds 95%;
## for two-sided hypotheses, the value tested against lies outside the 95%-CI.
## Posterior probabilities of point hypotheses assume equal prior probabilities.Re-do the other main model, the one with closeness_01 as
dependent variable, this time also with a difficulty_c
control covariate:
dist_self_mdl <- brm(bf(closeness_01 ~
# Fixed effects:
1 +
category +
self_contribution_c +
difficulty_c +
category:self_contribution_c +
# Random effects:
(1 +
category +
self_contribution_c +
category:self_contribution_c|participant) +
(1 + self_contribution_c|word),
phi ~ 1 + category),
data = df,
family = Beta,
# MCMC settings:
seed = 42,
init = 0,
cores = 4,
iter = 6000,
warmup = 3000,
save_pars = save_pars(all = TRUE), # for bayes factors
control = list(adapt_delta = 0.99))
# Save model:
save(dist_self_mdl,
file = '../models_E2/dist_self_mdl.Rdata')The corresponding null model:
dist_self_null <- brm(bf(closeness_01 ~
# Fixed effects:
1 +
category +
self_contribution_c +
difficulty_c +
# Random effects:
(1 +
category +
self_contribution_c +
category:self_contribution_c|participant) +
(1 + self_contribution_c|word),
phi ~ 1 + category),
data = df,
family = Beta,
# MCMC settings:
seed = 42,
init = 0,
cores = 4,
iter = 6000,
warmup = 3000,
save_pars = save_pars(all = TRUE), # for bayes factors
control = list(adapt_delta = 0.99))
# Save model:
save(dist_self_null,
file = '../models_E2/dist_self_null.Rdata')Load model:
load('../models_E2/dist_self_mdl.Rdata')
load('../models_E2/dist_self_null.Rdata')Show priors:
prior_summary(dist_self_mdl)## prior class coef
## (flat) b
## (flat) b categoryabstract
## (flat) b categoryabstract:self_contribution_c
## (flat) b difficulty_c
## (flat) b self_contribution_c
## (flat) b
## (flat) b categoryabstract
## student_t(3, 0, 2.5) Intercept
## student_t(3, 0, 2.5) Intercept
## lkj_corr_cholesky(1) L
## lkj_corr_cholesky(1) L
## lkj_corr_cholesky(1) L
## student_t(3, 0, 2.5) sd
## student_t(3, 0, 2.5) sd
## student_t(3, 0, 2.5) sd categoryabstract
## student_t(3, 0, 2.5) sd categoryabstract:self_contribution_c
## student_t(3, 0, 2.5) sd Intercept
## student_t(3, 0, 2.5) sd self_contribution_c
## student_t(3, 0, 2.5) sd
## student_t(3, 0, 2.5) sd Intercept
## student_t(3, 0, 2.5) sd self_contribution_c
## group resp dpar nlpar lb ub source
## default
## (vectorized)
## (vectorized)
## (vectorized)
## (vectorized)
## phi default
## phi (vectorized)
## default
## phi default
## default
## participant (vectorized)
## word (vectorized)
## 0 default
## participant 0 (vectorized)
## participant 0 (vectorized)
## participant 0 (vectorized)
## participant 0 (vectorized)
## participant 0 (vectorized)
## word 0 (vectorized)
## word 0 (vectorized)
## word 0 (vectorized)prior_summary(dist_self_null)## prior class coef
## (flat) b
## (flat) b categoryabstract
## (flat) b difficulty_c
## (flat) b self_contribution_c
## (flat) b
## (flat) b categoryabstract
## student_t(3, 0, 2.5) Intercept
## student_t(3, 0, 2.5) Intercept
## lkj_corr_cholesky(1) L
## lkj_corr_cholesky(1) L
## lkj_corr_cholesky(1) L
## student_t(3, 0, 2.5) sd
## student_t(3, 0, 2.5) sd
## student_t(3, 0, 2.5) sd categoryabstract
## student_t(3, 0, 2.5) sd categoryabstract:self_contribution_c
## student_t(3, 0, 2.5) sd Intercept
## student_t(3, 0, 2.5) sd self_contribution_c
## student_t(3, 0, 2.5) sd
## student_t(3, 0, 2.5) sd Intercept
## student_t(3, 0, 2.5) sd self_contribution_c
## group resp dpar nlpar lb ub source
## default
## (vectorized)
## (vectorized)
## (vectorized)
## phi default
## phi (vectorized)
## default
## phi default
## default
## participant (vectorized)
## word (vectorized)
## 0 default
## participant 0 (vectorized)
## participant 0 (vectorized)
## participant 0 (vectorized)
## participant 0 (vectorized)
## participant 0 (vectorized)
## word 0 (vectorized)
## word 0 (vectorized)
## word 0 (vectorized)Bayes factors for both:
# Compute:
dist_self_bf <- bayes_factor(dist_self_mdl, dist_self_null)
# Save:
save(dist_self_bf,
file = '../models_E2/dist_self_bf.RData')Show Bayes factor:
# Load:
load('../models_E2/dist_self_bf.RData')
# Show:
dist_self_bf## Estimated Bayes factor in favor of dist_self_mdl over dist_self_null: 0.03459Check posterior predictive checks of the mixed beta regression:
pp_check(dist_self_mdl, ndraws = 100)
Check this model:
dist_self_mdl## Family: beta
## Links: mu = logit; phi = log
## Formula: closeness_01 ~ 1 + category + self_contribution_c + difficulty_c + category:self_contribution_c + (1 + category + self_contribution_c + category:self_contribution_c | participant) + (1 + self_contribution_c | word)
## phi ~ 1 + category
## Data: df (Number of observations: 1032)
## Draws: 4 chains, each with iter = 6000; warmup = 3000; thin = 1;
## total post-warmup draws = 12000
##
## Group-Level Effects:
## ~participant (Number of levels: 129)
## Estimate
## sd(Intercept) 0.86
## sd(categoryabstract) 0.49
## sd(self_contribution_c) 0.02
## sd(categoryabstract:self_contribution_c) 0.01
## cor(Intercept,categoryabstract) -0.33
## cor(Intercept,self_contribution_c) 0.02
## cor(categoryabstract,self_contribution_c) -0.11
## cor(Intercept,categoryabstract:self_contribution_c) 0.01
## cor(categoryabstract,categoryabstract:self_contribution_c) 0.18
## cor(self_contribution_c,categoryabstract:self_contribution_c) -0.45
## Est.Error
## sd(Intercept) 0.07
## sd(categoryabstract) 0.07
## sd(self_contribution_c) 0.00
## sd(categoryabstract:self_contribution_c) 0.01
## cor(Intercept,categoryabstract) 0.12
## cor(Intercept,self_contribution_c) 0.13
## cor(categoryabstract,self_contribution_c) 0.15
## cor(Intercept,categoryabstract:self_contribution_c) 0.24
## cor(categoryabstract,categoryabstract:self_contribution_c) 0.25
## cor(self_contribution_c,categoryabstract:self_contribution_c) 0.30
## l-95% CI u-95% CI
## sd(Intercept) 0.74 1.00
## sd(categoryabstract) 0.35 0.62
## sd(self_contribution_c) 0.02 0.03
## sd(categoryabstract:self_contribution_c) 0.00 0.02
## cor(Intercept,categoryabstract) -0.54 -0.08
## cor(Intercept,self_contribution_c) -0.23 0.28
## cor(categoryabstract,self_contribution_c) -0.40 0.18
## cor(Intercept,categoryabstract:self_contribution_c) -0.52 0.49
## cor(categoryabstract,categoryabstract:self_contribution_c) -0.29 0.70
## cor(self_contribution_c,categoryabstract:self_contribution_c) -0.86 0.36
## Rhat Bulk_ESS
## sd(Intercept) 1.00 2783
## sd(categoryabstract) 1.00 991
## sd(self_contribution_c) 1.01 1072
## sd(categoryabstract:self_contribution_c) 1.01 465
## cor(Intercept,categoryabstract) 1.00 3371
## cor(Intercept,self_contribution_c) 1.00 4074
## cor(categoryabstract,self_contribution_c) 1.00 2718
## cor(Intercept,categoryabstract:self_contribution_c) 1.00 5985
## cor(categoryabstract,categoryabstract:self_contribution_c) 1.00 3369
## cor(self_contribution_c,categoryabstract:self_contribution_c) 1.00 1723
## Tail_ESS
## sd(Intercept) 5067
## sd(categoryabstract) 2754
## sd(self_contribution_c) 3057
## sd(categoryabstract:self_contribution_c) 1198
## cor(Intercept,categoryabstract) 6112
## cor(Intercept,self_contribution_c) 6854
## cor(categoryabstract,self_contribution_c) 4643
## cor(Intercept,categoryabstract:self_contribution_c) 3139
## cor(categoryabstract,categoryabstract:self_contribution_c) 2874
## cor(self_contribution_c,categoryabstract:self_contribution_c) 1847
##
## ~word (Number of levels: 32)
## Estimate Est.Error l-95% CI u-95% CI Rhat
## sd(Intercept) 0.07 0.03 0.02 0.12 1.00
## sd(self_contribution_c) 0.00 0.00 0.00 0.01 1.00
## cor(Intercept,self_contribution_c) 0.52 0.39 -0.50 0.98 1.00
## Bulk_ESS Tail_ESS
## sd(Intercept) 3554 2841
## sd(self_contribution_c) 3328 3876
## cor(Intercept,self_contribution_c) 4568 5221
##
## Population-Level Effects:
## Estimate Est.Error l-95% CI u-95% CI Rhat
## Intercept 0.93 0.08 0.76 1.09 1.00
## phi_Intercept 3.41 0.08 3.26 3.57 1.00
## categoryabstract -0.00 0.06 -0.13 0.12 1.00
## self_contribution_c 0.01 0.00 0.01 0.02 1.00
## difficulty_c -0.01 0.00 -0.01 -0.01 1.00
## categoryabstract:self_contribution_c 0.00 0.00 -0.01 0.01 1.00
## phi_categoryabstract -0.39 0.12 -0.62 -0.17 1.00
## Bulk_ESS Tail_ESS
## Intercept 1794 3425
## phi_Intercept 5543 8344
## categoryabstract 5843 7564
## self_contribution_c 5259 7560
## difficulty_c 13806 11659
## categoryabstract:self_contribution_c 7311 7923
## phi_categoryabstract 8706 9480
##
## Draws were sampled using sampling(NUTS). For each parameter, Bulk_ESS
## and Tail_ESS are effective sample size measures, and Rhat is the potential
## scale reduction factor on split chains (at convergence, Rhat = 1).Perform hypothesis tests on the fixed effects coefficient:
hypothesis(dist_self_mdl,
'categoryabstract > 0')## Hypothesis Tests for class b:
## Hypothesis Estimate Est.Error CI.Lower CI.Upper Evid.Ratio
## 1 (categoryabstract) > 0 0 0.06 -0.11 0.1 0.89
## Post.Prob Star
## 1 0.47
## ---
## 'CI': 90%-CI for one-sided and 95%-CI for two-sided hypotheses.
## '*': For one-sided hypotheses, the posterior probability exceeds 95%;
## for two-sided hypotheses, the value tested against lies outside the 95%-CI.
## Posterior probabilities of point hypotheses assume equal prior probabilities.hypothesis(dist_self_mdl,
'difficulty_c < 0')## Hypothesis Tests for class b:
## Hypothesis Estimate Est.Error CI.Lower CI.Upper Evid.Ratio Post.Prob
## 1 (difficulty_c) < 0 -0.01 0 -0.01 -0.01 Inf 1
## Star
## 1 *
## ---
## 'CI': 90%-CI for one-sided and 95%-CI for two-sided hypotheses.
## '*': For one-sided hypotheses, the posterior probability exceeds 95%;
## for two-sided hypotheses, the value tested against lies outside the 95%-CI.
## Posterior probabilities of point hypotheses assume equal prior probabilities.hypothesis(dist_self_mdl,
'self_contribution_c > 0')## Hypothesis Tests for class b:
## Hypothesis Estimate Est.Error CI.Lower CI.Upper Evid.Ratio
## 1 (self_contributio... > 0 0.01 0 0.01 0.02 5999
## Post.Prob Star
## 1 1 *
## ---
## 'CI': 90%-CI for one-sided and 95%-CI for two-sided hypotheses.
## '*': For one-sided hypotheses, the posterior probability exceeds 95%;
## for two-sided hypotheses, the value tested against lies outside the 95%-CI.
## Posterior probabilities of point hypotheses assume equal prior probabilities.hypothesis(dist_self_mdl,
'categoryabstract:self_contribution_c > 0')## Hypothesis Tests for class b:
## Hypothesis Estimate Est.Error CI.Lower CI.Upper Evid.Ratio
## 1 (categoryabstract... > 0 0 0 0 0.01 1.39
## Post.Prob Star
## 1 0.58
## ---
## 'CI': 90%-CI for one-sided and 95%-CI for two-sided hypotheses.
## '*': For one-sided hypotheses, the posterior probability exceeds 95%;
## for two-sided hypotheses, the value tested against lies outside the 95%-CI.
## Posterior probabilities of point hypotheses assume equal prior probabilities.13 Subcluster models: other-contribution
Do the main analysis of IOS with difficulty
as a covariate predictor, to control for this.
subcluster_mdl <- brm(IOS ~
# Fixed effects:
1 +
subcluster +
other_contribution_c +
difficulty_c +
subcluster:other_contribution_c +
# Random effects:
(1 +
subcluster +
other_contribution_c +
subcluster:other_contribution_c|participant) +
(1 + other_contribution_c|word),
data = df,
family = cumulative,
# MCMC settings:
seed = 42,
cores = 4,
iter = 6000,
warmup = 3000,
control = list(adapt_delta = 0.99))
# Save model:
save(subcluster_mdl,
file = '../models_E2/subcluster_mdl.Rdata')The corresponding null model:
subcluster_null <- brm(IOS ~
# Fixed effects:
1 +
subcluster +
other_contribution_c +
difficulty_c +
subcluster:other_contribution_c +
# Random effects:
(1 +
subcluster +
other_contribution_c +
subcluster:other_contribution_c|participant) +
(1 + other_contribution_c|word),
data = df,
family = cumulative,
# MCMC settings:
seed = 42,
cores = 4,
iter = 6000,
warmup = 3000,
control = list(adapt_delta = 0.99))
# Save model:
save(subcluster_null,
file = '../models_E2/subcluster_null.Rdata')Load model:
load('../models_E2/subcluster_mdl.Rdata')Show priors:
prior_summary(subcluster_mdl)## prior class coef
## (flat) b
## (flat) b difficulty_c
## (flat) b other_contribution_c
## (flat) b subclusterConc_an
## (flat) b subclusterConc_an:other_contribution_c
## (flat) b subclusterConc_in
## (flat) b subclusterConc_in:other_contribution_c
## (flat) b subclusterEM
## (flat) b subclusterEM:other_contribution_c
## (flat) b subclusterPS
## (flat) b subclusterPS:other_contribution_c
## (flat) b subclusterSS
## (flat) b subclusterSS:other_contribution_c
## student_t(3, 0, 2.5) Intercept
## student_t(3, 0, 2.5) Intercept 1
## student_t(3, 0, 2.5) Intercept 2
## student_t(3, 0, 2.5) Intercept 3
## student_t(3, 0, 2.5) Intercept 4
## student_t(3, 0, 2.5) Intercept 5
## lkj_corr_cholesky(1) L
## lkj_corr_cholesky(1) L
## lkj_corr_cholesky(1) L
## student_t(3, 0, 2.5) sd
## student_t(3, 0, 2.5) sd
## student_t(3, 0, 2.5) sd Intercept
## student_t(3, 0, 2.5) sd other_contribution_c
## student_t(3, 0, 2.5) sd subclusterConc_an
## student_t(3, 0, 2.5) sd subclusterConc_an:other_contribution_c
## student_t(3, 0, 2.5) sd subclusterConc_in
## student_t(3, 0, 2.5) sd subclusterConc_in:other_contribution_c
## student_t(3, 0, 2.5) sd subclusterEM
## student_t(3, 0, 2.5) sd subclusterEM:other_contribution_c
## student_t(3, 0, 2.5) sd subclusterPS
## student_t(3, 0, 2.5) sd subclusterPS:other_contribution_c
## student_t(3, 0, 2.5) sd subclusterSS
## student_t(3, 0, 2.5) sd subclusterSS:other_contribution_c
## student_t(3, 0, 2.5) sd
## student_t(3, 0, 2.5) sd Intercept
## student_t(3, 0, 2.5) sd other_contribution_c
## group resp dpar nlpar lb ub source
## default
## (vectorized)
## (vectorized)
## (vectorized)
## (vectorized)
## (vectorized)
## (vectorized)
## (vectorized)
## (vectorized)
## (vectorized)
## (vectorized)
## (vectorized)
## (vectorized)
## default
## (vectorized)
## (vectorized)
## (vectorized)
## (vectorized)
## (vectorized)
## default
## participant (vectorized)
## word (vectorized)
## 0 default
## participant 0 (vectorized)
## participant 0 (vectorized)
## participant 0 (vectorized)
## participant 0 (vectorized)
## participant 0 (vectorized)
## participant 0 (vectorized)
## participant 0 (vectorized)
## participant 0 (vectorized)
## participant 0 (vectorized)
## participant 0 (vectorized)
## participant 0 (vectorized)
## participant 0 (vectorized)
## participant 0 (vectorized)
## word 0 (vectorized)
## word 0 (vectorized)
## word 0 (vectorized)Check posterior predictive checks of the mixed beta regression:
pp_check(subcluster_mdl, ndraws = 100)
Check this model:
subcluster_mdl## Family: cumulative
## Links: mu = logit; disc = identity
## Formula: IOS ~ 1 + subcluster + other_contribution_c + difficulty_c + subcluster:other_contribution_c + (1 + subcluster + other_contribution_c + subcluster:other_contribution_c | participant) + (1 + other_contribution_c | word)
## Data: df (Number of observations: 1032)
## Draws: 4 chains, each with iter = 6000; warmup = 3000; thin = 1;
## total post-warmup draws = 12000
##
## Group-Level Effects:
## ~participant (Number of levels: 129)
## Estimate
## sd(Intercept) 2.92
## sd(subclusterConc_an) 1.41
## sd(subclusterConc_in) 1.61
## sd(subclusterEM) 0.50
## sd(subclusterPS) 0.70
## sd(subclusterSS) 0.60
## sd(other_contribution_c) 0.05
## sd(subclusterConc_an:other_contribution_c) 0.05
## sd(subclusterConc_in:other_contribution_c) 0.05
## sd(subclusterEM:other_contribution_c) 0.06
## sd(subclusterPS:other_contribution_c) 0.05
## sd(subclusterSS:other_contribution_c) 0.05
## cor(Intercept,subclusterConc_an) -0.09
## cor(Intercept,subclusterConc_in) -0.11
## cor(subclusterConc_an,subclusterConc_in) 0.66
## cor(Intercept,subclusterEM) -0.04
## cor(subclusterConc_an,subclusterEM) -0.07
## cor(subclusterConc_in,subclusterEM) -0.11
## cor(Intercept,subclusterPS) -0.02
## cor(subclusterConc_an,subclusterPS) -0.21
## cor(subclusterConc_in,subclusterPS) -0.18
## cor(subclusterEM,subclusterPS) 0.09
## cor(Intercept,subclusterSS) -0.02
## cor(subclusterConc_an,subclusterSS) 0.03
## cor(subclusterConc_in,subclusterSS) 0.05
## cor(subclusterEM,subclusterSS) 0.02
## cor(subclusterPS,subclusterSS) -0.00
## cor(Intercept,other_contribution_c) 0.04
## cor(subclusterConc_an,other_contribution_c) 0.01
## cor(subclusterConc_in,other_contribution_c) -0.06
## cor(subclusterEM,other_contribution_c) -0.08
## cor(subclusterPS,other_contribution_c) 0.01
## cor(subclusterSS,other_contribution_c) 0.07
## cor(Intercept,subclusterConc_an:other_contribution_c) 0.20
## cor(subclusterConc_an,subclusterConc_an:other_contribution_c) -0.04
## cor(subclusterConc_in,subclusterConc_an:other_contribution_c) -0.05
## cor(subclusterEM,subclusterConc_an:other_contribution_c) 0.00
## cor(subclusterPS,subclusterConc_an:other_contribution_c) -0.03
## cor(subclusterSS,subclusterConc_an:other_contribution_c) 0.03
## cor(other_contribution_c,subclusterConc_an:other_contribution_c) 0.05
## cor(Intercept,subclusterConc_in:other_contribution_c) 0.01
## cor(subclusterConc_an,subclusterConc_in:other_contribution_c) -0.01
## cor(subclusterConc_in,subclusterConc_in:other_contribution_c) 0.07
## cor(subclusterEM,subclusterConc_in:other_contribution_c) -0.06
## cor(subclusterPS,subclusterConc_in:other_contribution_c) 0.10
## cor(subclusterSS,subclusterConc_in:other_contribution_c) -0.07
## cor(other_contribution_c,subclusterConc_in:other_contribution_c) 0.00
## cor(subclusterConc_an:other_contribution_c,subclusterConc_in:other_contribution_c) 0.32
## cor(Intercept,subclusterEM:other_contribution_c) -0.04
## cor(subclusterConc_an,subclusterEM:other_contribution_c) 0.04
## cor(subclusterConc_in,subclusterEM:other_contribution_c) -0.13
## cor(subclusterEM,subclusterEM:other_contribution_c) 0.03
## cor(subclusterPS,subclusterEM:other_contribution_c) -0.10
## cor(subclusterSS,subclusterEM:other_contribution_c) 0.05
## cor(other_contribution_c,subclusterEM:other_contribution_c) -0.12
## cor(subclusterConc_an:other_contribution_c,subclusterEM:other_contribution_c) 0.02
## cor(subclusterConc_in:other_contribution_c,subclusterEM:other_contribution_c) -0.25
## cor(Intercept,subclusterPS:other_contribution_c) 0.15
## cor(subclusterConc_an,subclusterPS:other_contribution_c) 0.05
## cor(subclusterConc_in,subclusterPS:other_contribution_c) 0.12
## cor(subclusterEM,subclusterPS:other_contribution_c) -0.06
## cor(subclusterPS,subclusterPS:other_contribution_c) -0.06
## cor(subclusterSS,subclusterPS:other_contribution_c) 0.04
## cor(other_contribution_c,subclusterPS:other_contribution_c) 0.00
## cor(subclusterConc_an:other_contribution_c,subclusterPS:other_contribution_c) -0.06
## cor(subclusterConc_in:other_contribution_c,subclusterPS:other_contribution_c) -0.11
## cor(subclusterEM:other_contribution_c,subclusterPS:other_contribution_c) 0.08
## cor(Intercept,subclusterSS:other_contribution_c) 0.02
## cor(subclusterConc_an,subclusterSS:other_contribution_c) -0.06
## cor(subclusterConc_in,subclusterSS:other_contribution_c) -0.12
## cor(subclusterEM,subclusterSS:other_contribution_c) 0.04
## cor(subclusterPS,subclusterSS:other_contribution_c) 0.04
## cor(subclusterSS,subclusterSS:other_contribution_c) -0.05
## cor(other_contribution_c,subclusterSS:other_contribution_c) -0.07
## cor(subclusterConc_an:other_contribution_c,subclusterSS:other_contribution_c) -0.14
## cor(subclusterConc_in:other_contribution_c,subclusterSS:other_contribution_c) -0.12
## cor(subclusterEM:other_contribution_c,subclusterSS:other_contribution_c) 0.15
## cor(subclusterPS:other_contribution_c,subclusterSS:other_contribution_c) 0.14
## Est.Error
## sd(Intercept) 0.27
## sd(subclusterConc_an) 0.43
## sd(subclusterConc_in) 0.42
## sd(subclusterEM) 0.37
## sd(subclusterPS) 0.44
## sd(subclusterSS) 0.43
## sd(other_contribution_c) 0.01
## sd(subclusterConc_an:other_contribution_c) 0.03
## sd(subclusterConc_in:other_contribution_c) 0.02
## sd(subclusterEM:other_contribution_c) 0.02
## sd(subclusterPS:other_contribution_c) 0.03
## sd(subclusterSS:other_contribution_c) 0.03
## cor(Intercept,subclusterConc_an) 0.16
## cor(Intercept,subclusterConc_in) 0.16
## cor(subclusterConc_an,subclusterConc_in) 0.19
## cor(Intercept,subclusterEM) 0.25
## cor(subclusterConc_an,subclusterEM) 0.27
## cor(subclusterConc_in,subclusterEM) 0.27
## cor(Intercept,subclusterPS) 0.24
## cor(subclusterConc_an,subclusterPS) 0.27
## cor(subclusterConc_in,subclusterPS) 0.26
## cor(subclusterEM,subclusterPS) 0.28
## cor(Intercept,subclusterSS) 0.25
## cor(subclusterConc_an,subclusterSS) 0.27
## cor(subclusterConc_in,subclusterSS) 0.27
## cor(subclusterEM,subclusterSS) 0.28
## cor(subclusterPS,subclusterSS) 0.27
## cor(Intercept,other_contribution_c) 0.17
## cor(subclusterConc_an,other_contribution_c) 0.22
## cor(subclusterConc_in,other_contribution_c) 0.21
## cor(subclusterEM,other_contribution_c) 0.27
## cor(subclusterPS,other_contribution_c) 0.26
## cor(subclusterSS,other_contribution_c) 0.27
## cor(Intercept,subclusterConc_an:other_contribution_c) 0.22
## cor(subclusterConc_an,subclusterConc_an:other_contribution_c) 0.24
## cor(subclusterConc_in,subclusterConc_an:other_contribution_c) 0.24
## cor(subclusterEM,subclusterConc_an:other_contribution_c) 0.27
## cor(subclusterPS,subclusterConc_an:other_contribution_c) 0.27
## cor(subclusterSS,subclusterConc_an:other_contribution_c) 0.27
## cor(other_contribution_c,subclusterConc_an:other_contribution_c) 0.25
## cor(Intercept,subclusterConc_in:other_contribution_c) 0.21
## cor(subclusterConc_an,subclusterConc_in:other_contribution_c) 0.25
## cor(subclusterConc_in,subclusterConc_in:other_contribution_c) 0.23
## cor(subclusterEM,subclusterConc_in:other_contribution_c) 0.28
## cor(subclusterPS,subclusterConc_in:other_contribution_c) 0.27
## cor(subclusterSS,subclusterConc_in:other_contribution_c) 0.28
## cor(other_contribution_c,subclusterConc_in:other_contribution_c) 0.25
## cor(subclusterConc_an:other_contribution_c,subclusterConc_in:other_contribution_c) 0.30
## cor(Intercept,subclusterEM:other_contribution_c) 0.19
## cor(subclusterConc_an,subclusterEM:other_contribution_c) 0.23
## cor(subclusterConc_in,subclusterEM:other_contribution_c) 0.23
## cor(subclusterEM,subclusterEM:other_contribution_c) 0.27
## cor(subclusterPS,subclusterEM:other_contribution_c) 0.27
## cor(subclusterSS,subclusterEM:other_contribution_c) 0.27
## cor(other_contribution_c,subclusterEM:other_contribution_c) 0.24
## cor(subclusterConc_an:other_contribution_c,subclusterEM:other_contribution_c) 0.25
## cor(subclusterConc_in:other_contribution_c,subclusterEM:other_contribution_c) 0.25
## cor(Intercept,subclusterPS:other_contribution_c) 0.22
## cor(subclusterConc_an,subclusterPS:other_contribution_c) 0.25
## cor(subclusterConc_in,subclusterPS:other_contribution_c) 0.25
## cor(subclusterEM,subclusterPS:other_contribution_c) 0.28
## cor(subclusterPS,subclusterPS:other_contribution_c) 0.27
## cor(subclusterSS,subclusterPS:other_contribution_c) 0.27
## cor(other_contribution_c,subclusterPS:other_contribution_c) 0.25
## cor(subclusterConc_an:other_contribution_c,subclusterPS:other_contribution_c) 0.26
## cor(subclusterConc_in:other_contribution_c,subclusterPS:other_contribution_c) 0.26
## cor(subclusterEM:other_contribution_c,subclusterPS:other_contribution_c) 0.26
## cor(Intercept,subclusterSS:other_contribution_c) 0.23
## cor(subclusterConc_an,subclusterSS:other_contribution_c) 0.26
## cor(subclusterConc_in,subclusterSS:other_contribution_c) 0.26
## cor(subclusterEM,subclusterSS:other_contribution_c) 0.27
## cor(subclusterPS,subclusterSS:other_contribution_c) 0.27
## cor(subclusterSS,subclusterSS:other_contribution_c) 0.27
## cor(other_contribution_c,subclusterSS:other_contribution_c) 0.27
## cor(subclusterConc_an:other_contribution_c,subclusterSS:other_contribution_c) 0.27
## cor(subclusterConc_in:other_contribution_c,subclusterSS:other_contribution_c) 0.27
## cor(subclusterEM:other_contribution_c,subclusterSS:other_contribution_c) 0.27
## cor(subclusterPS:other_contribution_c,subclusterSS:other_contribution_c) 0.28
## l-95% CI
## sd(Intercept) 2.44
## sd(subclusterConc_an) 0.35
## sd(subclusterConc_in) 0.60
## sd(subclusterEM) 0.02
## sd(subclusterPS) 0.04
## sd(subclusterSS) 0.02
## sd(other_contribution_c) 0.02
## sd(subclusterConc_an:other_contribution_c) 0.00
## sd(subclusterConc_in:other_contribution_c) 0.01
## sd(subclusterEM:other_contribution_c) 0.02
## sd(subclusterPS:other_contribution_c) 0.00
## sd(subclusterSS:other_contribution_c) 0.00
## cor(Intercept,subclusterConc_an) -0.39
## cor(Intercept,subclusterConc_in) -0.40
## cor(subclusterConc_an,subclusterConc_in) 0.11
## cor(Intercept,subclusterEM) -0.51
## cor(subclusterConc_an,subclusterEM) -0.56
## cor(subclusterConc_in,subclusterEM) -0.60
## cor(Intercept,subclusterPS) -0.48
## cor(subclusterConc_an,subclusterPS) -0.68
## cor(subclusterConc_in,subclusterPS) -0.64
## cor(subclusterEM,subclusterPS) -0.47
## cor(Intercept,subclusterSS) -0.51
## cor(subclusterConc_an,subclusterSS) -0.49
## cor(subclusterConc_in,subclusterSS) -0.48
## cor(subclusterEM,subclusterSS) -0.51
## cor(subclusterPS,subclusterSS) -0.52
## cor(Intercept,other_contribution_c) -0.30
## cor(subclusterConc_an,other_contribution_c) -0.43
## cor(subclusterConc_in,other_contribution_c) -0.46
## cor(subclusterEM,other_contribution_c) -0.57
## cor(subclusterPS,other_contribution_c) -0.48
## cor(subclusterSS,other_contribution_c) -0.47
## cor(Intercept,subclusterConc_an:other_contribution_c) -0.28
## cor(subclusterConc_an,subclusterConc_an:other_contribution_c) -0.49
## cor(subclusterConc_in,subclusterConc_an:other_contribution_c) -0.51
## cor(subclusterEM,subclusterConc_an:other_contribution_c) -0.51
## cor(subclusterPS,subclusterConc_an:other_contribution_c) -0.54
## cor(subclusterSS,subclusterConc_an:other_contribution_c) -0.51
## cor(other_contribution_c,subclusterConc_an:other_contribution_c) -0.43
## cor(Intercept,subclusterConc_in:other_contribution_c) -0.41
## cor(subclusterConc_an,subclusterConc_in:other_contribution_c) -0.48
## cor(subclusterConc_in,subclusterConc_in:other_contribution_c) -0.39
## cor(subclusterEM,subclusterConc_in:other_contribution_c) -0.58
## cor(subclusterPS,subclusterConc_in:other_contribution_c) -0.44
## cor(subclusterSS,subclusterConc_in:other_contribution_c) -0.58
## cor(other_contribution_c,subclusterConc_in:other_contribution_c) -0.46
## cor(subclusterConc_an:other_contribution_c,subclusterConc_in:other_contribution_c) -0.33
## cor(Intercept,subclusterEM:other_contribution_c) -0.42
## cor(subclusterConc_an,subclusterEM:other_contribution_c) -0.43
## cor(subclusterConc_in,subclusterEM:other_contribution_c) -0.56
## cor(subclusterEM,subclusterEM:other_contribution_c) -0.50
## cor(subclusterPS,subclusterEM:other_contribution_c) -0.59
## cor(subclusterSS,subclusterEM:other_contribution_c) -0.48
## cor(other_contribution_c,subclusterEM:other_contribution_c) -0.56
## cor(subclusterConc_an:other_contribution_c,subclusterEM:other_contribution_c) -0.47
## cor(subclusterConc_in:other_contribution_c,subclusterEM:other_contribution_c) -0.68
## cor(Intercept,subclusterPS:other_contribution_c) -0.29
## cor(subclusterConc_an,subclusterPS:other_contribution_c) -0.44
## cor(subclusterConc_in,subclusterPS:other_contribution_c) -0.38
## cor(subclusterEM,subclusterPS:other_contribution_c) -0.58
## cor(subclusterPS,subclusterPS:other_contribution_c) -0.56
## cor(subclusterSS,subclusterPS:other_contribution_c) -0.49
## cor(other_contribution_c,subclusterPS:other_contribution_c) -0.48
## cor(subclusterConc_an:other_contribution_c,subclusterPS:other_contribution_c) -0.54
## cor(subclusterConc_in:other_contribution_c,subclusterPS:other_contribution_c) -0.58
## cor(subclusterEM:other_contribution_c,subclusterPS:other_contribution_c) -0.44
## cor(Intercept,subclusterSS:other_contribution_c) -0.45
## cor(subclusterConc_an,subclusterSS:other_contribution_c) -0.55
## cor(subclusterConc_in,subclusterSS:other_contribution_c) -0.59
## cor(subclusterEM,subclusterSS:other_contribution_c) -0.49
## cor(subclusterPS,subclusterSS:other_contribution_c) -0.49
## cor(subclusterSS,subclusterSS:other_contribution_c) -0.57
## cor(other_contribution_c,subclusterSS:other_contribution_c) -0.58
## cor(subclusterConc_an:other_contribution_c,subclusterSS:other_contribution_c) -0.62
## cor(subclusterConc_in:other_contribution_c,subclusterSS:other_contribution_c) -0.61
## cor(subclusterEM:other_contribution_c,subclusterSS:other_contribution_c) -0.40
## cor(subclusterPS:other_contribution_c,subclusterSS:other_contribution_c) -0.44
## u-95% CI
## sd(Intercept) 3.50
## sd(subclusterConc_an) 2.14
## sd(subclusterConc_in) 2.34
## sd(subclusterEM) 1.35
## sd(subclusterPS) 1.62
## sd(subclusterSS) 1.56
## sd(other_contribution_c) 0.08
## sd(subclusterConc_an:other_contribution_c) 0.10
## sd(subclusterConc_in:other_contribution_c) 0.10
## sd(subclusterEM:other_contribution_c) 0.10
## sd(subclusterPS:other_contribution_c) 0.10
## sd(subclusterSS:other_contribution_c) 0.10
## cor(Intercept,subclusterConc_an) 0.25
## cor(Intercept,subclusterConc_in) 0.22
## cor(subclusterConc_an,subclusterConc_in) 0.89
## cor(Intercept,subclusterEM) 0.47
## cor(subclusterConc_an,subclusterEM) 0.46
## cor(subclusterConc_in,subclusterEM) 0.44
## cor(Intercept,subclusterPS) 0.47
## cor(subclusterConc_an,subclusterPS) 0.37
## cor(subclusterConc_in,subclusterPS) 0.38
## cor(subclusterEM,subclusterPS) 0.60
## cor(Intercept,subclusterSS) 0.48
## cor(subclusterConc_an,subclusterSS) 0.54
## cor(subclusterConc_in,subclusterSS) 0.56
## cor(subclusterEM,subclusterSS) 0.54
## cor(subclusterPS,subclusterSS) 0.53
## cor(Intercept,other_contribution_c) 0.37
## cor(subclusterConc_an,other_contribution_c) 0.42
## cor(subclusterConc_in,other_contribution_c) 0.34
## cor(subclusterEM,other_contribution_c) 0.46
## cor(subclusterPS,other_contribution_c) 0.53
## cor(subclusterSS,other_contribution_c) 0.58
## cor(Intercept,subclusterConc_an:other_contribution_c) 0.58
## cor(subclusterConc_an,subclusterConc_an:other_contribution_c) 0.43
## cor(subclusterConc_in,subclusterConc_an:other_contribution_c) 0.43
## cor(subclusterEM,subclusterConc_an:other_contribution_c) 0.52
## cor(subclusterPS,subclusterConc_an:other_contribution_c) 0.49
## cor(subclusterSS,subclusterConc_an:other_contribution_c) 0.55
## cor(other_contribution_c,subclusterConc_an:other_contribution_c) 0.53
## cor(Intercept,subclusterConc_in:other_contribution_c) 0.41
## cor(subclusterConc_an,subclusterConc_in:other_contribution_c) 0.47
## cor(subclusterConc_in,subclusterConc_in:other_contribution_c) 0.51
## cor(subclusterEM,subclusterConc_in:other_contribution_c) 0.48
## cor(subclusterPS,subclusterConc_in:other_contribution_c) 0.59
## cor(subclusterSS,subclusterConc_in:other_contribution_c) 0.48
## cor(other_contribution_c,subclusterConc_in:other_contribution_c) 0.51
## cor(subclusterConc_an:other_contribution_c,subclusterConc_in:other_contribution_c) 0.78
## cor(Intercept,subclusterEM:other_contribution_c) 0.35
## cor(subclusterConc_an,subclusterEM:other_contribution_c) 0.48
## cor(subclusterConc_in,subclusterEM:other_contribution_c) 0.32
## cor(subclusterEM,subclusterEM:other_contribution_c) 0.54
## cor(subclusterPS,subclusterEM:other_contribution_c) 0.45
## cor(subclusterSS,subclusterEM:other_contribution_c) 0.56
## cor(other_contribution_c,subclusterEM:other_contribution_c) 0.39
## cor(subclusterConc_an:other_contribution_c,subclusterEM:other_contribution_c) 0.50
## cor(subclusterConc_in:other_contribution_c,subclusterEM:other_contribution_c) 0.30
## cor(Intercept,subclusterPS:other_contribution_c) 0.56
## cor(subclusterConc_an,subclusterPS:other_contribution_c) 0.53
## cor(subclusterConc_in,subclusterPS:other_contribution_c) 0.58
## cor(subclusterEM,subclusterPS:other_contribution_c) 0.48
## cor(subclusterPS,subclusterPS:other_contribution_c) 0.46
## cor(subclusterSS,subclusterPS:other_contribution_c) 0.56
## cor(other_contribution_c,subclusterPS:other_contribution_c) 0.50
## cor(subclusterConc_an:other_contribution_c,subclusterPS:other_contribution_c) 0.44
## cor(subclusterConc_in:other_contribution_c,subclusterPS:other_contribution_c) 0.42
## cor(subclusterEM:other_contribution_c,subclusterPS:other_contribution_c) 0.56
## cor(Intercept,subclusterSS:other_contribution_c) 0.46
## cor(subclusterConc_an,subclusterSS:other_contribution_c) 0.45
## cor(subclusterConc_in,subclusterSS:other_contribution_c) 0.40
## cor(subclusterEM,subclusterSS:other_contribution_c) 0.57
## cor(subclusterPS,subclusterSS:other_contribution_c) 0.56
## cor(subclusterSS,subclusterSS:other_contribution_c) 0.48
## cor(other_contribution_c,subclusterSS:other_contribution_c) 0.47
## cor(subclusterConc_an:other_contribution_c,subclusterSS:other_contribution_c) 0.42
## cor(subclusterConc_in:other_contribution_c,subclusterSS:other_contribution_c) 0.43
## cor(subclusterEM:other_contribution_c,subclusterSS:other_contribution_c) 0.62
## cor(subclusterPS:other_contribution_c,subclusterSS:other_contribution_c) 0.64
## Rhat
## sd(Intercept) 1.00
## sd(subclusterConc_an) 1.00
## sd(subclusterConc_in) 1.00
## sd(subclusterEM) 1.00
## sd(subclusterPS) 1.00
## sd(subclusterSS) 1.00
## sd(other_contribution_c) 1.00
## sd(subclusterConc_an:other_contribution_c) 1.01
## sd(subclusterConc_in:other_contribution_c) 1.00
## sd(subclusterEM:other_contribution_c) 1.00
## sd(subclusterPS:other_contribution_c) 1.00
## sd(subclusterSS:other_contribution_c) 1.00
## cor(Intercept,subclusterConc_an) 1.00
## cor(Intercept,subclusterConc_in) 1.00
## cor(subclusterConc_an,subclusterConc_in) 1.00
## cor(Intercept,subclusterEM) 1.00
## cor(subclusterConc_an,subclusterEM) 1.00
## cor(subclusterConc_in,subclusterEM) 1.00
## cor(Intercept,subclusterPS) 1.00
## cor(subclusterConc_an,subclusterPS) 1.00
## cor(subclusterConc_in,subclusterPS) 1.00
## cor(subclusterEM,subclusterPS) 1.00
## cor(Intercept,subclusterSS) 1.00
## cor(subclusterConc_an,subclusterSS) 1.00
## cor(subclusterConc_in,subclusterSS) 1.00
## cor(subclusterEM,subclusterSS) 1.00
## cor(subclusterPS,subclusterSS) 1.00
## cor(Intercept,other_contribution_c) 1.00
## cor(subclusterConc_an,other_contribution_c) 1.00
## cor(subclusterConc_in,other_contribution_c) 1.00
## cor(subclusterEM,other_contribution_c) 1.00
## cor(subclusterPS,other_contribution_c) 1.00
## cor(subclusterSS,other_contribution_c) 1.00
## cor(Intercept,subclusterConc_an:other_contribution_c) 1.00
## cor(subclusterConc_an,subclusterConc_an:other_contribution_c) 1.00
## cor(subclusterConc_in,subclusterConc_an:other_contribution_c) 1.00
## cor(subclusterEM,subclusterConc_an:other_contribution_c) 1.00
## cor(subclusterPS,subclusterConc_an:other_contribution_c) 1.00
## cor(subclusterSS,subclusterConc_an:other_contribution_c) 1.00
## cor(other_contribution_c,subclusterConc_an:other_contribution_c) 1.00
## cor(Intercept,subclusterConc_in:other_contribution_c) 1.00
## cor(subclusterConc_an,subclusterConc_in:other_contribution_c) 1.00
## cor(subclusterConc_in,subclusterConc_in:other_contribution_c) 1.00
## cor(subclusterEM,subclusterConc_in:other_contribution_c) 1.00
## cor(subclusterPS,subclusterConc_in:other_contribution_c) 1.00
## cor(subclusterSS,subclusterConc_in:other_contribution_c) 1.00
## cor(other_contribution_c,subclusterConc_in:other_contribution_c) 1.00
## cor(subclusterConc_an:other_contribution_c,subclusterConc_in:other_contribution_c) 1.00
## cor(Intercept,subclusterEM:other_contribution_c) 1.00
## cor(subclusterConc_an,subclusterEM:other_contribution_c) 1.00
## cor(subclusterConc_in,subclusterEM:other_contribution_c) 1.00
## cor(subclusterEM,subclusterEM:other_contribution_c) 1.00
## cor(subclusterPS,subclusterEM:other_contribution_c) 1.00
## cor(subclusterSS,subclusterEM:other_contribution_c) 1.00
## cor(other_contribution_c,subclusterEM:other_contribution_c) 1.00
## cor(subclusterConc_an:other_contribution_c,subclusterEM:other_contribution_c) 1.00
## cor(subclusterConc_in:other_contribution_c,subclusterEM:other_contribution_c) 1.00
## cor(Intercept,subclusterPS:other_contribution_c) 1.00
## cor(subclusterConc_an,subclusterPS:other_contribution_c) 1.00
## cor(subclusterConc_in,subclusterPS:other_contribution_c) 1.00
## cor(subclusterEM,subclusterPS:other_contribution_c) 1.00
## cor(subclusterPS,subclusterPS:other_contribution_c) 1.00
## cor(subclusterSS,subclusterPS:other_contribution_c) 1.00
## cor(other_contribution_c,subclusterPS:other_contribution_c) 1.00
## cor(subclusterConc_an:other_contribution_c,subclusterPS:other_contribution_c) 1.00
## cor(subclusterConc_in:other_contribution_c,subclusterPS:other_contribution_c) 1.00
## cor(subclusterEM:other_contribution_c,subclusterPS:other_contribution_c) 1.00
## cor(Intercept,subclusterSS:other_contribution_c) 1.00
## cor(subclusterConc_an,subclusterSS:other_contribution_c) 1.00
## cor(subclusterConc_in,subclusterSS:other_contribution_c) 1.00
## cor(subclusterEM,subclusterSS:other_contribution_c) 1.00
## cor(subclusterPS,subclusterSS:other_contribution_c) 1.00
## cor(subclusterSS,subclusterSS:other_contribution_c) 1.00
## cor(other_contribution_c,subclusterSS:other_contribution_c) 1.00
## cor(subclusterConc_an:other_contribution_c,subclusterSS:other_contribution_c) 1.00
## cor(subclusterConc_in:other_contribution_c,subclusterSS:other_contribution_c) 1.00
## cor(subclusterEM:other_contribution_c,subclusterSS:other_contribution_c) 1.00
## cor(subclusterPS:other_contribution_c,subclusterSS:other_contribution_c) 1.00
## Bulk_ESS
## sd(Intercept) 3287
## sd(subclusterConc_an) 727
## sd(subclusterConc_in) 967
## sd(subclusterEM) 1692
## sd(subclusterPS) 1956
## sd(subclusterSS) 2401
## sd(other_contribution_c) 1985
## sd(subclusterConc_an:other_contribution_c) 761
## sd(subclusterConc_in:other_contribution_c) 745
## sd(subclusterEM:other_contribution_c) 2302
## sd(subclusterPS:other_contribution_c) 1829
## sd(subclusterSS:other_contribution_c) 2098
## cor(Intercept,subclusterConc_an) 7264
## cor(Intercept,subclusterConc_in) 7404
## cor(subclusterConc_an,subclusterConc_in) 1110
## cor(Intercept,subclusterEM) 17472
## cor(subclusterConc_an,subclusterEM) 9347
## cor(subclusterConc_in,subclusterEM) 8370
## cor(Intercept,subclusterPS) 13544
## cor(subclusterConc_an,subclusterPS) 5026
## cor(subclusterConc_in,subclusterPS) 7553
## cor(subclusterEM,subclusterPS) 6523
## cor(Intercept,subclusterSS) 18693
## cor(subclusterConc_an,subclusterSS) 10395
## cor(subclusterConc_in,subclusterSS) 10305
## cor(subclusterEM,subclusterSS) 9133
## cor(subclusterPS,subclusterSS) 9961
## cor(Intercept,other_contribution_c) 8664
## cor(subclusterConc_an,other_contribution_c) 2849
## cor(subclusterConc_in,other_contribution_c) 3603
## cor(subclusterEM,other_contribution_c) 2005
## cor(subclusterPS,other_contribution_c) 2466
## cor(subclusterSS,other_contribution_c) 2369
## cor(Intercept,subclusterConc_an:other_contribution_c) 7834
## cor(subclusterConc_an,subclusterConc_an:other_contribution_c) 6297
## cor(subclusterConc_in,subclusterConc_an:other_contribution_c) 6988
## cor(subclusterEM,subclusterConc_an:other_contribution_c) 4485
## cor(subclusterPS,subclusterConc_an:other_contribution_c) 4027
## cor(subclusterSS,subclusterConc_an:other_contribution_c) 5120
## cor(other_contribution_c,subclusterConc_an:other_contribution_c) 6447
## cor(Intercept,subclusterConc_in:other_contribution_c) 7864
## cor(subclusterConc_an,subclusterConc_in:other_contribution_c) 3973
## cor(subclusterConc_in,subclusterConc_in:other_contribution_c) 6143
## cor(subclusterEM,subclusterConc_in:other_contribution_c) 3232
## cor(subclusterPS,subclusterConc_in:other_contribution_c) 3388
## cor(subclusterSS,subclusterConc_in:other_contribution_c) 4435
## cor(other_contribution_c,subclusterConc_in:other_contribution_c) 5645
## cor(subclusterConc_an:other_contribution_c,subclusterConc_in:other_contribution_c) 1073
## cor(Intercept,subclusterEM:other_contribution_c) 9676
## cor(subclusterConc_an,subclusterEM:other_contribution_c) 4970
## cor(subclusterConc_in,subclusterEM:other_contribution_c) 5590
## cor(subclusterEM,subclusterEM:other_contribution_c) 3713
## cor(subclusterPS,subclusterEM:other_contribution_c) 3583
## cor(subclusterSS,subclusterEM:other_contribution_c) 4956
## cor(other_contribution_c,subclusterEM:other_contribution_c) 4133
## cor(subclusterConc_an:other_contribution_c,subclusterEM:other_contribution_c) 5100
## cor(subclusterConc_in:other_contribution_c,subclusterEM:other_contribution_c) 3922
## cor(Intercept,subclusterPS:other_contribution_c) 10101
## cor(subclusterConc_an,subclusterPS:other_contribution_c) 7772
## cor(subclusterConc_in,subclusterPS:other_contribution_c) 6854
## cor(subclusterEM,subclusterPS:other_contribution_c) 5488
## cor(subclusterPS,subclusterPS:other_contribution_c) 5515
## cor(subclusterSS,subclusterPS:other_contribution_c) 6328
## cor(other_contribution_c,subclusterPS:other_contribution_c) 6901
## cor(subclusterConc_an:other_contribution_c,subclusterPS:other_contribution_c) 6573
## cor(subclusterConc_in:other_contribution_c,subclusterPS:other_contribution_c) 5640
## cor(subclusterEM:other_contribution_c,subclusterPS:other_contribution_c) 6623
## cor(Intercept,subclusterSS:other_contribution_c) 15392
## cor(subclusterConc_an,subclusterSS:other_contribution_c) 8784
## cor(subclusterConc_in,subclusterSS:other_contribution_c) 8346
## cor(subclusterEM,subclusterSS:other_contribution_c) 6621
## cor(subclusterPS,subclusterSS:other_contribution_c) 6934
## cor(subclusterSS,subclusterSS:other_contribution_c) 7400
## cor(other_contribution_c,subclusterSS:other_contribution_c) 8725
## cor(subclusterConc_an:other_contribution_c,subclusterSS:other_contribution_c) 5415
## cor(subclusterConc_in:other_contribution_c,subclusterSS:other_contribution_c) 6761
## cor(subclusterEM:other_contribution_c,subclusterSS:other_contribution_c) 6706
## cor(subclusterPS:other_contribution_c,subclusterSS:other_contribution_c) 5164
## Tail_ESS
## sd(Intercept) 6113
## sd(subclusterConc_an) 649
## sd(subclusterConc_in) 919
## sd(subclusterEM) 3110
## sd(subclusterPS) 4528
## sd(subclusterSS) 5071
## sd(other_contribution_c) 1450
## sd(subclusterConc_an:other_contribution_c) 2442
## sd(subclusterConc_in:other_contribution_c) 2289
## sd(subclusterEM:other_contribution_c) 2509
## sd(subclusterPS:other_contribution_c) 3768
## sd(subclusterSS:other_contribution_c) 4115
## cor(Intercept,subclusterConc_an) 5795
## cor(Intercept,subclusterConc_in) 5939
## cor(subclusterConc_an,subclusterConc_in) 858
## cor(Intercept,subclusterEM) 8904
## cor(subclusterConc_an,subclusterEM) 8144
## cor(subclusterConc_in,subclusterEM) 8543
## cor(Intercept,subclusterPS) 8104
## cor(subclusterConc_an,subclusterPS) 6743
## cor(subclusterConc_in,subclusterPS) 8769
## cor(subclusterEM,subclusterPS) 8351
## cor(Intercept,subclusterSS) 9233
## cor(subclusterConc_an,subclusterSS) 9228
## cor(subclusterConc_in,subclusterSS) 9112
## cor(subclusterEM,subclusterSS) 9012
## cor(subclusterPS,subclusterSS) 9421
## cor(Intercept,other_contribution_c) 8263
## cor(subclusterConc_an,other_contribution_c) 4891
## cor(subclusterConc_in,other_contribution_c) 6654
## cor(subclusterEM,other_contribution_c) 5413
## cor(subclusterPS,other_contribution_c) 4643
## cor(subclusterSS,other_contribution_c) 4316
## cor(Intercept,subclusterConc_an:other_contribution_c) 5572
## cor(subclusterConc_an,subclusterConc_an:other_contribution_c) 8077
## cor(subclusterConc_in,subclusterConc_an:other_contribution_c) 8141
## cor(subclusterEM,subclusterConc_an:other_contribution_c) 7488
## cor(subclusterPS,subclusterConc_an:other_contribution_c) 6818
## cor(subclusterSS,subclusterConc_an:other_contribution_c) 7832
## cor(other_contribution_c,subclusterConc_an:other_contribution_c) 9251
## cor(Intercept,subclusterConc_in:other_contribution_c) 7120
## cor(subclusterConc_an,subclusterConc_in:other_contribution_c) 7217
## cor(subclusterConc_in,subclusterConc_in:other_contribution_c) 7365
## cor(subclusterEM,subclusterConc_in:other_contribution_c) 6533
## cor(subclusterPS,subclusterConc_in:other_contribution_c) 6102
## cor(subclusterSS,subclusterConc_in:other_contribution_c) 6904
## cor(other_contribution_c,subclusterConc_in:other_contribution_c) 8912
## cor(subclusterConc_an:other_contribution_c,subclusterConc_in:other_contribution_c) 4016
## cor(Intercept,subclusterEM:other_contribution_c) 8749
## cor(subclusterConc_an,subclusterEM:other_contribution_c) 6703
## cor(subclusterConc_in,subclusterEM:other_contribution_c) 6640
## cor(subclusterEM,subclusterEM:other_contribution_c) 6988
## cor(subclusterPS,subclusterEM:other_contribution_c) 6391
## cor(subclusterSS,subclusterEM:other_contribution_c) 7329
## cor(other_contribution_c,subclusterEM:other_contribution_c) 7653
## cor(subclusterConc_an:other_contribution_c,subclusterEM:other_contribution_c) 8476
## cor(subclusterConc_in:other_contribution_c,subclusterEM:other_contribution_c) 5517
## cor(Intercept,subclusterPS:other_contribution_c) 8781
## cor(subclusterConc_an,subclusterPS:other_contribution_c) 9027
## cor(subclusterConc_in,subclusterPS:other_contribution_c) 7782
## cor(subclusterEM,subclusterPS:other_contribution_c) 8559
## cor(subclusterPS,subclusterPS:other_contribution_c) 8841
## cor(subclusterSS,subclusterPS:other_contribution_c) 8974
## cor(other_contribution_c,subclusterPS:other_contribution_c) 9826
## cor(subclusterConc_an:other_contribution_c,subclusterPS:other_contribution_c) 9547
## cor(subclusterConc_in:other_contribution_c,subclusterPS:other_contribution_c) 8372
## cor(subclusterEM:other_contribution_c,subclusterPS:other_contribution_c) 7883
## cor(Intercept,subclusterSS:other_contribution_c) 8555
## cor(subclusterConc_an,subclusterSS:other_contribution_c) 7367
## cor(subclusterConc_in,subclusterSS:other_contribution_c) 9132
## cor(subclusterEM,subclusterSS:other_contribution_c) 8486
## cor(subclusterPS,subclusterSS:other_contribution_c) 9553
## cor(subclusterSS,subclusterSS:other_contribution_c) 9531
## cor(other_contribution_c,subclusterSS:other_contribution_c) 9152
## cor(subclusterConc_an:other_contribution_c,subclusterSS:other_contribution_c) 9599
## cor(subclusterConc_in:other_contribution_c,subclusterSS:other_contribution_c) 10038
## cor(subclusterEM:other_contribution_c,subclusterSS:other_contribution_c) 8659
## cor(subclusterPS:other_contribution_c,subclusterSS:other_contribution_c) 9094
##
## ~word (Number of levels: 32)
## Estimate Est.Error l-95% CI u-95% CI Rhat
## sd(Intercept) 0.13 0.09 0.01 0.34 1.00
## sd(other_contribution_c) 0.01 0.01 0.00 0.03 1.00
## cor(Intercept,other_contribution_c) 0.08 0.56 -0.92 0.96 1.00
## Bulk_ESS Tail_ESS
## sd(Intercept) 5007 6932
## sd(other_contribution_c) 3211 5674
## cor(Intercept,other_contribution_c) 5232 8046
##
## Population-Level Effects:
## Estimate Est.Error l-95% CI u-95% CI
## Intercept[1] -6.15 0.46 -7.07 -5.27
## Intercept[2] -2.06 0.35 -2.76 -1.39
## Intercept[3] 0.96 0.34 0.29 1.64
## Intercept[4] 3.47 0.38 2.75 4.24
## Intercept[5] 6.42 0.47 5.54 7.37
## subclusterConc_an -0.08 0.29 -0.65 0.49
## subclusterConc_in -0.06 0.31 -0.66 0.54
## subclusterEM 0.03 0.29 -0.54 0.62
## subclusterPS -0.02 0.30 -0.61 0.59
## subclusterSS -0.23 0.34 -0.89 0.43
## other_contribution_c 0.07 0.02 0.04 0.10
## difficulty_c -0.03 0.00 -0.04 -0.03
## subclusterConc_an:other_contribution_c -0.01 0.02 -0.05 0.02
## subclusterConc_in:other_contribution_c 0.00 0.02 -0.03 0.03
## subclusterEM:other_contribution_c -0.01 0.02 -0.04 0.03
## subclusterPS:other_contribution_c 0.01 0.02 -0.03 0.04
## subclusterSS:other_contribution_c 0.01 0.02 -0.04 0.05
## Rhat Bulk_ESS Tail_ESS
## Intercept[1] 1.00 3748 6467
## Intercept[2] 1.00 3940 6742
## Intercept[3] 1.00 4156 6519
## Intercept[4] 1.00 4025 6536
## Intercept[5] 1.00 3885 6845
## subclusterConc_an 1.00 7950 8891
## subclusterConc_in 1.00 8299 8522
## subclusterEM 1.00 9786 9426
## subclusterPS 1.00 10542 9609
## subclusterSS 1.00 9487 8554
## other_contribution_c 1.00 6072 7177
## difficulty_c 1.00 8617 9326
## subclusterConc_an:other_contribution_c 1.00 6696 7599
## subclusterConc_in:other_contribution_c 1.00 6587 8152
## subclusterEM:other_contribution_c 1.00 7556 7390
## subclusterPS:other_contribution_c 1.00 8699 7894
## subclusterSS:other_contribution_c 1.00 8492 8670
##
## Family Specific Parameters:
## Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
## disc 1.00 0.00 1.00 1.00 NA NA NA
##
## Draws were sampled using sampling(NUTS). For each parameter, Bulk_ESS
## and Tail_ESS are effective sample size measures, and Rhat is the potential
## scale reduction factor on split chains (at convergence, Rhat = 1).Perform hypothesis tests on the fixed effects coefficient:
hypothesis(subcluster_mdl,
'other_contribution_c > 0')## Hypothesis Tests for class b:
## Hypothesis Estimate Est.Error CI.Lower CI.Upper Evid.Ratio
## 1 (other_contributi... > 0 0.07 0.02 0.05 0.1 11999
## Post.Prob Star
## 1 1 *
## ---
## 'CI': 90%-CI for one-sided and 95%-CI for two-sided hypotheses.
## '*': For one-sided hypotheses, the posterior probability exceeds 95%;
## for two-sided hypotheses, the value tested against lies outside the 95%-CI.
## Posterior probabilities of point hypotheses assume equal prior probabilities.hypothesis(subcluster_mdl,
'difficulty_c < 0')## Hypothesis Tests for class b:
## Hypothesis Estimate Est.Error CI.Lower CI.Upper Evid.Ratio Post.Prob
## 1 (difficulty_c) < 0 -0.03 0 -0.04 -0.03 Inf 1
## Star
## 1 *
## ---
## 'CI': 90%-CI for one-sided and 95%-CI for two-sided hypotheses.
## '*': For one-sided hypotheses, the posterior probability exceeds 95%;
## for two-sided hypotheses, the value tested against lies outside the 95%-CI.
## Posterior probabilities of point hypotheses assume equal prior probabilities.hypothesis(subcluster_mdl,
'subclusterConc_an:other_contribution_c < 0') # PSTQ is reference## Hypothesis Tests for class b:
## Hypothesis Estimate Est.Error CI.Lower CI.Upper Evid.Ratio
## 1 (subclusterConc_a... < 0 -0.01 0.02 -0.04 0.02 3.54
## Post.Prob Star
## 1 0.78
## ---
## 'CI': 90%-CI for one-sided and 95%-CI for two-sided hypotheses.
## '*': For one-sided hypotheses, the posterior probability exceeds 95%;
## for two-sided hypotheses, the value tested against lies outside the 95%-CI.
## Posterior probabilities of point hypotheses assume equal prior probabilities.hypothesis(subcluster_mdl,
'subclusterConc_in:other_contribution_c < 0') # PSTQ is reference## Hypothesis Tests for class b:
## Hypothesis Estimate Est.Error CI.Lower CI.Upper Evid.Ratio
## 1 (subclusterConc_i... < 0 0 0.02 -0.03 0.03 1.01
## Post.Prob Star
## 1 0.5
## ---
## 'CI': 90%-CI for one-sided and 95%-CI for two-sided hypotheses.
## '*': For one-sided hypotheses, the posterior probability exceeds 95%;
## for two-sided hypotheses, the value tested against lies outside the 95%-CI.
## Posterior probabilities of point hypotheses assume equal prior probabilities.hypothesis(subcluster_mdl,
'subclusterEM:other_contribution_c < 0') # PSTQ is reference## Hypothesis Tests for class b:
## Hypothesis Estimate Est.Error CI.Lower CI.Upper Evid.Ratio
## 1 (subclusterEM:oth... < 0 -0.01 0.02 -0.04 0.02 2.22
## Post.Prob Star
## 1 0.69
## ---
## 'CI': 90%-CI for one-sided and 95%-CI for two-sided hypotheses.
## '*': For one-sided hypotheses, the posterior probability exceeds 95%;
## for two-sided hypotheses, the value tested against lies outside the 95%-CI.
## Posterior probabilities of point hypotheses assume equal prior probabilities.hypothesis(subcluster_mdl,
'subclusterPS:other_contribution_c < 0') # PSTQ is reference## Hypothesis Tests for class b:
## Hypothesis Estimate Est.Error CI.Lower CI.Upper Evid.Ratio
## 1 (subclusterPS:oth... < 0 0.01 0.02 -0.02 0.04 0.52
## Post.Prob Star
## 1 0.34
## ---
## 'CI': 90%-CI for one-sided and 95%-CI for two-sided hypotheses.
## '*': For one-sided hypotheses, the posterior probability exceeds 95%;
## for two-sided hypotheses, the value tested against lies outside the 95%-CI.
## Posterior probabilities of point hypotheses assume equal prior probabilities.hypothesis(subcluster_mdl,
'subclusterSS:other_contribution_c < 0') # PSTQ is reference## Hypothesis Tests for class b:
## Hypothesis Estimate Est.Error CI.Lower CI.Upper Evid.Ratio
## 1 (subclusterSS:oth... < 0 0.01 0.02 -0.03 0.04 0.67
## Post.Prob Star
## 1 0.4
## ---
## 'CI': 90%-CI for one-sided and 95%-CI for two-sided hypotheses.
## '*': For one-sided hypotheses, the posterior probability exceeds 95%;
## for two-sided hypotheses, the value tested against lies outside the 95%-CI.
## Posterior probabilities of point hypotheses assume equal prior probabilities.Re-do the other main model, the one with closeness_01 as
dependent variable, this time also with a difficulty_c
control covariate:
subcluster_dist_mdl <- brm(bf(closeness_01 ~
# Fixed effects:
1 +
subcluster +
other_contribution_c +
difficulty_c +
subcluster:other_contribution_c +
# Random effects:
(1 +
subcluster +
other_contribution_c +
subcluster:other_contribution_c|participant) +
(1 + other_contribution_c|word),
phi ~ 1),
data = df,
family = Beta,
# MCMC settings:
seed = 42,
init = 0,
cores = 4,
iter = 6000,
warmup = 3000,
control = list(adapt_delta = 0.99))
# Save model:
save(subcluster_dist_mdl,
file = '../models_E2/subcluster_dist_mdl.RData')Load model:
load('../models_E2/subcluster_dist_mdl.Rdata')Show priors:
prior_summary(subcluster_dist_mdl)## prior class coef
## (flat) b
## (flat) b difficulty_c
## (flat) b other_contribution_c
## (flat) b subclusterConc_an
## (flat) b subclusterConc_an:other_contribution_c
## (flat) b subclusterConc_in
## (flat) b subclusterConc_in:other_contribution_c
## (flat) b subclusterEM
## (flat) b subclusterEM:other_contribution_c
## (flat) b subclusterPS
## (flat) b subclusterPS:other_contribution_c
## (flat) b subclusterSS
## (flat) b subclusterSS:other_contribution_c
## student_t(3, 0, 2.5) Intercept
## student_t(3, 0, 2.5) Intercept
## lkj_corr_cholesky(1) L
## lkj_corr_cholesky(1) L
## lkj_corr_cholesky(1) L
## student_t(3, 0, 2.5) sd
## student_t(3, 0, 2.5) sd
## student_t(3, 0, 2.5) sd Intercept
## student_t(3, 0, 2.5) sd other_contribution_c
## student_t(3, 0, 2.5) sd subclusterConc_an
## student_t(3, 0, 2.5) sd subclusterConc_an:other_contribution_c
## student_t(3, 0, 2.5) sd subclusterConc_in
## student_t(3, 0, 2.5) sd subclusterConc_in:other_contribution_c
## student_t(3, 0, 2.5) sd subclusterEM
## student_t(3, 0, 2.5) sd subclusterEM:other_contribution_c
## student_t(3, 0, 2.5) sd subclusterPS
## student_t(3, 0, 2.5) sd subclusterPS:other_contribution_c
## student_t(3, 0, 2.5) sd subclusterSS
## student_t(3, 0, 2.5) sd subclusterSS:other_contribution_c
## student_t(3, 0, 2.5) sd
## student_t(3, 0, 2.5) sd Intercept
## student_t(3, 0, 2.5) sd other_contribution_c
## group resp dpar nlpar lb ub source
## default
## (vectorized)
## (vectorized)
## (vectorized)
## (vectorized)
## (vectorized)
## (vectorized)
## (vectorized)
## (vectorized)
## (vectorized)
## (vectorized)
## (vectorized)
## (vectorized)
## default
## phi default
## default
## participant (vectorized)
## word (vectorized)
## 0 default
## participant 0 (vectorized)
## participant 0 (vectorized)
## participant 0 (vectorized)
## participant 0 (vectorized)
## participant 0 (vectorized)
## participant 0 (vectorized)
## participant 0 (vectorized)
## participant 0 (vectorized)
## participant 0 (vectorized)
## participant 0 (vectorized)
## participant 0 (vectorized)
## participant 0 (vectorized)
## participant 0 (vectorized)
## word 0 (vectorized)
## word 0 (vectorized)
## word 0 (vectorized)Check posterior predictive checks of the mixed beta regression:
pp_check(subcluster_dist_mdl, ndraws = 100)
Check this model:
subcluster_dist_mdl## Family: beta
## Links: mu = logit; phi = log
## Formula: closeness_01 ~ 1 + subcluster + other_contribution_c + difficulty_c + subcluster:other_contribution_c + (1 + subcluster + other_contribution_c + subcluster:other_contribution_c | participant) + (1 + other_contribution_c | word)
## phi ~ 1
## Data: df (Number of observations: 1032)
## Draws: 4 chains, each with iter = 6000; warmup = 3000; thin = 1;
## total post-warmup draws = 12000
##
## Group-Level Effects:
## ~participant (Number of levels: 129)
## Estimate
## sd(Intercept) 0.86
## sd(subclusterConc_an) 0.42
## sd(subclusterConc_in) 0.30
## sd(subclusterEM) 0.09
## sd(subclusterPS) 0.27
## sd(subclusterSS) 0.12
## sd(other_contribution_c) 0.02
## sd(subclusterConc_an:other_contribution_c) 0.02
## sd(subclusterConc_in:other_contribution_c) 0.02
## sd(subclusterEM:other_contribution_c) 0.01
## sd(subclusterPS:other_contribution_c) 0.02
## sd(subclusterSS:other_contribution_c) 0.01
## cor(Intercept,subclusterConc_an) -0.03
## cor(Intercept,subclusterConc_in) -0.05
## cor(subclusterConc_an,subclusterConc_in) 0.67
## cor(Intercept,subclusterEM) -0.00
## cor(subclusterConc_an,subclusterEM) 0.03
## cor(subclusterConc_in,subclusterEM) 0.03
## cor(Intercept,subclusterPS) 0.00
## cor(subclusterConc_an,subclusterPS) -0.11
## cor(subclusterConc_in,subclusterPS) -0.03
## cor(subclusterEM,subclusterPS) 0.02
## cor(Intercept,subclusterSS) 0.07
## cor(subclusterConc_an,subclusterSS) 0.02
## cor(subclusterConc_in,subclusterSS) -0.02
## cor(subclusterEM,subclusterSS) 0.04
## cor(subclusterPS,subclusterSS) 0.04
## cor(Intercept,other_contribution_c) -0.01
## cor(subclusterConc_an,other_contribution_c) 0.10
## cor(subclusterConc_in,other_contribution_c) -0.02
## cor(subclusterEM,other_contribution_c) 0.02
## cor(subclusterPS,other_contribution_c) -0.11
## cor(subclusterSS,other_contribution_c) -0.10
## cor(Intercept,subclusterConc_an:other_contribution_c) 0.14
## cor(subclusterConc_an,subclusterConc_an:other_contribution_c) -0.27
## cor(subclusterConc_in,subclusterConc_an:other_contribution_c) -0.07
## cor(subclusterEM,subclusterConc_an:other_contribution_c) -0.01
## cor(subclusterPS,subclusterConc_an:other_contribution_c) -0.03
## cor(subclusterSS,subclusterConc_an:other_contribution_c) 0.08
## cor(other_contribution_c,subclusterConc_an:other_contribution_c) -0.30
## cor(Intercept,subclusterConc_in:other_contribution_c) -0.01
## cor(subclusterConc_an,subclusterConc_in:other_contribution_c) 0.03
## cor(subclusterConc_in,subclusterConc_in:other_contribution_c) 0.12
## cor(subclusterEM,subclusterConc_in:other_contribution_c) 0.00
## cor(subclusterPS,subclusterConc_in:other_contribution_c) -0.11
## cor(subclusterSS,subclusterConc_in:other_contribution_c) 0.15
## cor(other_contribution_c,subclusterConc_in:other_contribution_c) -0.37
## cor(subclusterConc_an:other_contribution_c,subclusterConc_in:other_contribution_c) 0.54
## cor(Intercept,subclusterEM:other_contribution_c) 0.12
## cor(subclusterConc_an,subclusterEM:other_contribution_c) 0.02
## cor(subclusterConc_in,subclusterEM:other_contribution_c) 0.03
## cor(subclusterEM,subclusterEM:other_contribution_c) 0.09
## cor(subclusterPS,subclusterEM:other_contribution_c) -0.08
## cor(subclusterSS,subclusterEM:other_contribution_c) -0.10
## cor(other_contribution_c,subclusterEM:other_contribution_c) 0.01
## cor(subclusterConc_an:other_contribution_c,subclusterEM:other_contribution_c) 0.01
## cor(subclusterConc_in:other_contribution_c,subclusterEM:other_contribution_c) 0.07
## cor(Intercept,subclusterPS:other_contribution_c) 0.06
## cor(subclusterConc_an,subclusterPS:other_contribution_c) -0.10
## cor(subclusterConc_in,subclusterPS:other_contribution_c) -0.07
## cor(subclusterEM,subclusterPS:other_contribution_c) -0.02
## cor(subclusterPS,subclusterPS:other_contribution_c) 0.33
## cor(subclusterSS,subclusterPS:other_contribution_c) 0.05
## cor(other_contribution_c,subclusterPS:other_contribution_c) -0.00
## cor(subclusterConc_an:other_contribution_c,subclusterPS:other_contribution_c) -0.11
## cor(subclusterConc_in:other_contribution_c,subclusterPS:other_contribution_c) -0.11
## cor(subclusterEM:other_contribution_c,subclusterPS:other_contribution_c) -0.05
## cor(Intercept,subclusterSS:other_contribution_c) -0.10
## cor(subclusterConc_an,subclusterSS:other_contribution_c) 0.14
## cor(subclusterConc_in,subclusterSS:other_contribution_c) 0.13
## cor(subclusterEM,subclusterSS:other_contribution_c) -0.00
## cor(subclusterPS,subclusterSS:other_contribution_c) 0.02
## cor(subclusterSS,subclusterSS:other_contribution_c) 0.02
## cor(other_contribution_c,subclusterSS:other_contribution_c) 0.05
## cor(subclusterConc_an:other_contribution_c,subclusterSS:other_contribution_c) 0.00
## cor(subclusterConc_in:other_contribution_c,subclusterSS:other_contribution_c) 0.08
## cor(subclusterEM:other_contribution_c,subclusterSS:other_contribution_c) 0.05
## cor(subclusterPS:other_contribution_c,subclusterSS:other_contribution_c) 0.13
## Est.Error
## sd(Intercept) 0.07
## sd(subclusterConc_an) 0.15
## sd(subclusterConc_in) 0.15
## sd(subclusterEM) 0.07
## sd(subclusterPS) 0.13
## sd(subclusterSS) 0.08
## sd(other_contribution_c) 0.00
## sd(subclusterConc_an:other_contribution_c) 0.01
## sd(subclusterConc_in:other_contribution_c) 0.01
## sd(subclusterEM:other_contribution_c) 0.00
## sd(subclusterPS:other_contribution_c) 0.01
## sd(subclusterSS:other_contribution_c) 0.00
## cor(Intercept,subclusterConc_an) 0.17
## cor(Intercept,subclusterConc_in) 0.19
## cor(subclusterConc_an,subclusterConc_in) 0.31
## cor(Intercept,subclusterEM) 0.26
## cor(subclusterConc_an,subclusterEM) 0.27
## cor(subclusterConc_in,subclusterEM) 0.27
## cor(Intercept,subclusterPS) 0.21
## cor(subclusterConc_an,subclusterPS) 0.24
## cor(subclusterConc_in,subclusterPS) 0.25
## cor(subclusterEM,subclusterPS) 0.28
## cor(Intercept,subclusterSS) 0.25
## cor(subclusterConc_an,subclusterSS) 0.26
## cor(subclusterConc_in,subclusterSS) 0.26
## cor(subclusterEM,subclusterSS) 0.27
## cor(subclusterPS,subclusterSS) 0.28
## cor(Intercept,other_contribution_c) 0.13
## cor(subclusterConc_an,other_contribution_c) 0.17
## cor(subclusterConc_in,other_contribution_c) 0.20
## cor(subclusterEM,other_contribution_c) 0.26
## cor(subclusterPS,other_contribution_c) 0.22
## cor(subclusterSS,other_contribution_c) 0.26
## cor(Intercept,subclusterConc_an:other_contribution_c) 0.18
## cor(subclusterConc_an,subclusterConc_an:other_contribution_c) 0.19
## cor(subclusterConc_in,subclusterConc_an:other_contribution_c) 0.22
## cor(subclusterEM,subclusterConc_an:other_contribution_c) 0.27
## cor(subclusterPS,subclusterConc_an:other_contribution_c) 0.25
## cor(subclusterSS,subclusterConc_an:other_contribution_c) 0.27
## cor(other_contribution_c,subclusterConc_an:other_contribution_c) 0.23
## cor(Intercept,subclusterConc_in:other_contribution_c) 0.18
## cor(subclusterConc_an,subclusterConc_in:other_contribution_c) 0.26
## cor(subclusterConc_in,subclusterConc_in:other_contribution_c) 0.23
## cor(subclusterEM,subclusterConc_in:other_contribution_c) 0.26
## cor(subclusterPS,subclusterConc_in:other_contribution_c) 0.25
## cor(subclusterSS,subclusterConc_in:other_contribution_c) 0.27
## cor(other_contribution_c,subclusterConc_in:other_contribution_c) 0.24
## cor(subclusterConc_an:other_contribution_c,subclusterConc_in:other_contribution_c) 0.34
## cor(Intercept,subclusterEM:other_contribution_c) 0.18
## cor(subclusterConc_an,subclusterEM:other_contribution_c) 0.22
## cor(subclusterConc_in,subclusterEM:other_contribution_c) 0.23
## cor(subclusterEM,subclusterEM:other_contribution_c) 0.27
## cor(subclusterPS,subclusterEM:other_contribution_c) 0.24
## cor(subclusterSS,subclusterEM:other_contribution_c) 0.27
## cor(other_contribution_c,subclusterEM:other_contribution_c) 0.22
## cor(subclusterConc_an:other_contribution_c,subclusterEM:other_contribution_c) 0.24
## cor(subclusterConc_in:other_contribution_c,subclusterEM:other_contribution_c) 0.23
## cor(Intercept,subclusterPS:other_contribution_c) 0.16
## cor(subclusterConc_an,subclusterPS:other_contribution_c) 0.20
## cor(subclusterConc_in,subclusterPS:other_contribution_c) 0.23
## cor(subclusterEM,subclusterPS:other_contribution_c) 0.27
## cor(subclusterPS,subclusterPS:other_contribution_c) 0.23
## cor(subclusterSS,subclusterPS:other_contribution_c) 0.27
## cor(other_contribution_c,subclusterPS:other_contribution_c) 0.19
## cor(subclusterConc_an:other_contribution_c,subclusterPS:other_contribution_c) 0.21
## cor(subclusterConc_in:other_contribution_c,subclusterPS:other_contribution_c) 0.22
## cor(subclusterEM:other_contribution_c,subclusterPS:other_contribution_c) 0.21
## cor(Intercept,subclusterSS:other_contribution_c) 0.25
## cor(subclusterConc_an,subclusterSS:other_contribution_c) 0.28
## cor(subclusterConc_in,subclusterSS:other_contribution_c) 0.28
## cor(subclusterEM,subclusterSS:other_contribution_c) 0.28
## cor(subclusterPS,subclusterSS:other_contribution_c) 0.27
## cor(subclusterSS,subclusterSS:other_contribution_c) 0.27
## cor(other_contribution_c,subclusterSS:other_contribution_c) 0.27
## cor(subclusterConc_an:other_contribution_c,subclusterSS:other_contribution_c) 0.28
## cor(subclusterConc_in:other_contribution_c,subclusterSS:other_contribution_c) 0.27
## cor(subclusterEM:other_contribution_c,subclusterSS:other_contribution_c) 0.27
## cor(subclusterPS:other_contribution_c,subclusterSS:other_contribution_c) 0.28
## l-95% CI
## sd(Intercept) 0.74
## sd(subclusterConc_an) 0.12
## sd(subclusterConc_in) 0.01
## sd(subclusterEM) 0.00
## sd(subclusterPS) 0.03
## sd(subclusterSS) 0.01
## sd(other_contribution_c) 0.01
## sd(subclusterConc_an:other_contribution_c) 0.00
## sd(subclusterConc_in:other_contribution_c) 0.00
## sd(subclusterEM:other_contribution_c) 0.01
## sd(subclusterPS:other_contribution_c) 0.01
## sd(subclusterSS:other_contribution_c) 0.00
## cor(Intercept,subclusterConc_an) -0.31
## cor(Intercept,subclusterConc_in) -0.38
## cor(subclusterConc_an,subclusterConc_in) -0.18
## cor(Intercept,subclusterEM) -0.49
## cor(subclusterConc_an,subclusterEM) -0.50
## cor(subclusterConc_in,subclusterEM) -0.50
## cor(Intercept,subclusterPS) -0.41
## cor(subclusterConc_an,subclusterPS) -0.56
## cor(subclusterConc_in,subclusterPS) -0.51
## cor(subclusterEM,subclusterPS) -0.53
## cor(Intercept,subclusterSS) -0.43
## cor(subclusterConc_an,subclusterSS) -0.48
## cor(subclusterConc_in,subclusterSS) -0.52
## cor(subclusterEM,subclusterSS) -0.50
## cor(subclusterPS,subclusterSS) -0.50
## cor(Intercept,other_contribution_c) -0.27
## cor(subclusterConc_an,other_contribution_c) -0.22
## cor(subclusterConc_in,other_contribution_c) -0.42
## cor(subclusterEM,other_contribution_c) -0.49
## cor(subclusterPS,other_contribution_c) -0.53
## cor(subclusterSS,other_contribution_c) -0.57
## cor(Intercept,subclusterConc_an:other_contribution_c) -0.21
## cor(subclusterConc_an,subclusterConc_an:other_contribution_c) -0.61
## cor(subclusterConc_in,subclusterConc_an:other_contribution_c) -0.48
## cor(subclusterEM,subclusterConc_an:other_contribution_c) -0.52
## cor(subclusterPS,subclusterConc_an:other_contribution_c) -0.50
## cor(subclusterSS,subclusterConc_an:other_contribution_c) -0.47
## cor(other_contribution_c,subclusterConc_an:other_contribution_c) -0.64
## cor(Intercept,subclusterConc_in:other_contribution_c) -0.42
## cor(subclusterConc_an,subclusterConc_in:other_contribution_c) -0.46
## cor(subclusterConc_in,subclusterConc_in:other_contribution_c) -0.37
## cor(subclusterEM,subclusterConc_in:other_contribution_c) -0.50
## cor(subclusterPS,subclusterConc_in:other_contribution_c) -0.56
## cor(subclusterSS,subclusterConc_in:other_contribution_c) -0.42
## cor(other_contribution_c,subclusterConc_in:other_contribution_c) -0.70
## cor(subclusterConc_an:other_contribution_c,subclusterConc_in:other_contribution_c) -0.28
## cor(Intercept,subclusterEM:other_contribution_c) -0.24
## cor(subclusterConc_an,subclusterEM:other_contribution_c) -0.40
## cor(subclusterConc_in,subclusterEM:other_contribution_c) -0.42
## cor(subclusterEM,subclusterEM:other_contribution_c) -0.45
## cor(subclusterPS,subclusterEM:other_contribution_c) -0.53
## cor(subclusterSS,subclusterEM:other_contribution_c) -0.60
## cor(other_contribution_c,subclusterEM:other_contribution_c) -0.42
## cor(subclusterConc_an:other_contribution_c,subclusterEM:other_contribution_c) -0.46
## cor(subclusterConc_in:other_contribution_c,subclusterEM:other_contribution_c) -0.41
## cor(Intercept,subclusterPS:other_contribution_c) -0.24
## cor(subclusterConc_an,subclusterPS:other_contribution_c) -0.48
## cor(subclusterConc_in,subclusterPS:other_contribution_c) -0.49
## cor(subclusterEM,subclusterPS:other_contribution_c) -0.54
## cor(subclusterPS,subclusterPS:other_contribution_c) -0.18
## cor(subclusterSS,subclusterPS:other_contribution_c) -0.49
## cor(other_contribution_c,subclusterPS:other_contribution_c) -0.37
## cor(subclusterConc_an:other_contribution_c,subclusterPS:other_contribution_c) -0.52
## cor(subclusterConc_in:other_contribution_c,subclusterPS:other_contribution_c) -0.53
## cor(subclusterEM:other_contribution_c,subclusterPS:other_contribution_c) -0.46
## cor(Intercept,subclusterSS:other_contribution_c) -0.56
## cor(subclusterConc_an,subclusterSS:other_contribution_c) -0.43
## cor(subclusterConc_in,subclusterSS:other_contribution_c) -0.45
## cor(subclusterEM,subclusterSS:other_contribution_c) -0.53
## cor(subclusterPS,subclusterSS:other_contribution_c) -0.51
## cor(subclusterSS,subclusterSS:other_contribution_c) -0.51
## cor(other_contribution_c,subclusterSS:other_contribution_c) -0.49
## cor(subclusterConc_an:other_contribution_c,subclusterSS:other_contribution_c) -0.52
## cor(subclusterConc_in:other_contribution_c,subclusterSS:other_contribution_c) -0.45
## cor(subclusterEM:other_contribution_c,subclusterSS:other_contribution_c) -0.48
## cor(subclusterPS:other_contribution_c,subclusterSS:other_contribution_c) -0.45
## u-95% CI
## sd(Intercept) 0.99
## sd(subclusterConc_an) 0.65
## sd(subclusterConc_in) 0.52
## sd(subclusterEM) 0.26
## sd(subclusterPS) 0.54
## sd(subclusterSS) 0.29
## sd(other_contribution_c) 0.03
## sd(subclusterConc_an:other_contribution_c) 0.03
## sd(subclusterConc_in:other_contribution_c) 0.03
## sd(subclusterEM:other_contribution_c) 0.02
## sd(subclusterPS:other_contribution_c) 0.04
## sd(subclusterSS:other_contribution_c) 0.02
## cor(Intercept,subclusterConc_an) 0.35
## cor(Intercept,subclusterConc_in) 0.38
## cor(subclusterConc_an,subclusterConc_in) 0.94
## cor(Intercept,subclusterEM) 0.51
## cor(subclusterConc_an,subclusterEM) 0.54
## cor(subclusterConc_in,subclusterEM) 0.54
## cor(Intercept,subclusterPS) 0.43
## cor(subclusterConc_an,subclusterPS) 0.38
## cor(subclusterConc_in,subclusterPS) 0.47
## cor(subclusterEM,subclusterPS) 0.55
## cor(Intercept,subclusterSS) 0.54
## cor(subclusterConc_an,subclusterSS) 0.51
## cor(subclusterConc_in,subclusterSS) 0.49
## cor(subclusterEM,subclusterSS) 0.56
## cor(subclusterPS,subclusterSS) 0.55
## cor(Intercept,other_contribution_c) 0.25
## cor(subclusterConc_an,other_contribution_c) 0.44
## cor(subclusterConc_in,other_contribution_c) 0.37
## cor(subclusterEM,other_contribution_c) 0.51
## cor(subclusterPS,other_contribution_c) 0.35
## cor(subclusterSS,other_contribution_c) 0.45
## cor(Intercept,subclusterConc_an:other_contribution_c) 0.51
## cor(subclusterConc_an,subclusterConc_an:other_contribution_c) 0.14
## cor(subclusterConc_in,subclusterConc_an:other_contribution_c) 0.37
## cor(subclusterEM,subclusterConc_an:other_contribution_c) 0.50
## cor(subclusterPS,subclusterConc_an:other_contribution_c) 0.47
## cor(subclusterSS,subclusterConc_an:other_contribution_c) 0.57
## cor(other_contribution_c,subclusterConc_an:other_contribution_c) 0.25
## cor(Intercept,subclusterConc_in:other_contribution_c) 0.32
## cor(subclusterConc_an,subclusterConc_in:other_contribution_c) 0.54
## cor(subclusterConc_in,subclusterConc_in:other_contribution_c) 0.56
## cor(subclusterEM,subclusterConc_in:other_contribution_c) 0.51
## cor(subclusterPS,subclusterConc_in:other_contribution_c) 0.42
## cor(subclusterSS,subclusterConc_in:other_contribution_c) 0.62
## cor(other_contribution_c,subclusterConc_in:other_contribution_c) 0.21
## cor(subclusterConc_an:other_contribution_c,subclusterConc_in:other_contribution_c) 0.91
## cor(Intercept,subclusterEM:other_contribution_c) 0.46
## cor(subclusterConc_an,subclusterEM:other_contribution_c) 0.45
## cor(subclusterConc_in,subclusterEM:other_contribution_c) 0.48
## cor(subclusterEM,subclusterEM:other_contribution_c) 0.59
## cor(subclusterPS,subclusterEM:other_contribution_c) 0.41
## cor(subclusterSS,subclusterEM:other_contribution_c) 0.43
## cor(other_contribution_c,subclusterEM:other_contribution_c) 0.45
## cor(subclusterConc_an:other_contribution_c,subclusterEM:other_contribution_c) 0.47
## cor(subclusterConc_in:other_contribution_c,subclusterEM:other_contribution_c) 0.48
## cor(Intercept,subclusterPS:other_contribution_c) 0.40
## cor(subclusterConc_an,subclusterPS:other_contribution_c) 0.32
## cor(subclusterConc_in,subclusterPS:other_contribution_c) 0.43
## cor(subclusterEM,subclusterPS:other_contribution_c) 0.51
## cor(subclusterPS,subclusterPS:other_contribution_c) 0.71
## cor(subclusterSS,subclusterPS:other_contribution_c) 0.56
## cor(other_contribution_c,subclusterPS:other_contribution_c) 0.38
## cor(subclusterConc_an:other_contribution_c,subclusterPS:other_contribution_c) 0.35
## cor(subclusterConc_in:other_contribution_c,subclusterPS:other_contribution_c) 0.33
## cor(subclusterEM:other_contribution_c,subclusterPS:other_contribution_c) 0.36
## cor(Intercept,subclusterSS:other_contribution_c) 0.42
## cor(subclusterConc_an,subclusterSS:other_contribution_c) 0.64
## cor(subclusterConc_in,subclusterSS:other_contribution_c) 0.63
## cor(subclusterEM,subclusterSS:other_contribution_c) 0.53
## cor(subclusterPS,subclusterSS:other_contribution_c) 0.54
## cor(subclusterSS,subclusterSS:other_contribution_c) 0.54
## cor(other_contribution_c,subclusterSS:other_contribution_c) 0.55
## cor(subclusterConc_an:other_contribution_c,subclusterSS:other_contribution_c) 0.53
## cor(subclusterConc_in:other_contribution_c,subclusterSS:other_contribution_c) 0.58
## cor(subclusterEM:other_contribution_c,subclusterSS:other_contribution_c) 0.55
## cor(subclusterPS:other_contribution_c,subclusterSS:other_contribution_c) 0.64
## Rhat
## sd(Intercept) 1.00
## sd(subclusterConc_an) 1.01
## sd(subclusterConc_in) 1.02
## sd(subclusterEM) 1.00
## sd(subclusterPS) 1.01
## sd(subclusterSS) 1.00
## sd(other_contribution_c) 1.01
## sd(subclusterConc_an:other_contribution_c) 1.02
## sd(subclusterConc_in:other_contribution_c) 1.02
## sd(subclusterEM:other_contribution_c) 1.00
## sd(subclusterPS:other_contribution_c) 1.01
## sd(subclusterSS:other_contribution_c) 1.00
## cor(Intercept,subclusterConc_an) 1.01
## cor(Intercept,subclusterConc_in) 1.01
## cor(subclusterConc_an,subclusterConc_in) 1.01
## cor(Intercept,subclusterEM) 1.00
## cor(subclusterConc_an,subclusterEM) 1.00
## cor(subclusterConc_in,subclusterEM) 1.00
## cor(Intercept,subclusterPS) 1.00
## cor(subclusterConc_an,subclusterPS) 1.00
## cor(subclusterConc_in,subclusterPS) 1.00
## cor(subclusterEM,subclusterPS) 1.00
## cor(Intercept,subclusterSS) 1.00
## cor(subclusterConc_an,subclusterSS) 1.00
## cor(subclusterConc_in,subclusterSS) 1.00
## cor(subclusterEM,subclusterSS) 1.00
## cor(subclusterPS,subclusterSS) 1.00
## cor(Intercept,other_contribution_c) 1.00
## cor(subclusterConc_an,other_contribution_c) 1.00
## cor(subclusterConc_in,other_contribution_c) 1.01
## cor(subclusterEM,other_contribution_c) 1.01
## cor(subclusterPS,other_contribution_c) 1.00
## cor(subclusterSS,other_contribution_c) 1.01
## cor(Intercept,subclusterConc_an:other_contribution_c) 1.00
## cor(subclusterConc_an,subclusterConc_an:other_contribution_c) 1.00
## cor(subclusterConc_in,subclusterConc_an:other_contribution_c) 1.00
## cor(subclusterEM,subclusterConc_an:other_contribution_c) 1.00
## cor(subclusterPS,subclusterConc_an:other_contribution_c) 1.00
## cor(subclusterSS,subclusterConc_an:other_contribution_c) 1.00
## cor(other_contribution_c,subclusterConc_an:other_contribution_c) 1.01
## cor(Intercept,subclusterConc_in:other_contribution_c) 1.00
## cor(subclusterConc_an,subclusterConc_in:other_contribution_c) 1.01
## cor(subclusterConc_in,subclusterConc_in:other_contribution_c) 1.00
## cor(subclusterEM,subclusterConc_in:other_contribution_c) 1.00
## cor(subclusterPS,subclusterConc_in:other_contribution_c) 1.00
## cor(subclusterSS,subclusterConc_in:other_contribution_c) 1.00
## cor(other_contribution_c,subclusterConc_in:other_contribution_c) 1.01
## cor(subclusterConc_an:other_contribution_c,subclusterConc_in:other_contribution_c) 1.02
## cor(Intercept,subclusterEM:other_contribution_c) 1.00
## cor(subclusterConc_an,subclusterEM:other_contribution_c) 1.00
## cor(subclusterConc_in,subclusterEM:other_contribution_c) 1.00
## cor(subclusterEM,subclusterEM:other_contribution_c) 1.00
## cor(subclusterPS,subclusterEM:other_contribution_c) 1.00
## cor(subclusterSS,subclusterEM:other_contribution_c) 1.00
## cor(other_contribution_c,subclusterEM:other_contribution_c) 1.00
## cor(subclusterConc_an:other_contribution_c,subclusterEM:other_contribution_c) 1.00
## cor(subclusterConc_in:other_contribution_c,subclusterEM:other_contribution_c) 1.00
## cor(Intercept,subclusterPS:other_contribution_c) 1.00
## cor(subclusterConc_an,subclusterPS:other_contribution_c) 1.00
## cor(subclusterConc_in,subclusterPS:other_contribution_c) 1.00
## cor(subclusterEM,subclusterPS:other_contribution_c) 1.00
## cor(subclusterPS,subclusterPS:other_contribution_c) 1.00
## cor(subclusterSS,subclusterPS:other_contribution_c) 1.00
## cor(other_contribution_c,subclusterPS:other_contribution_c) 1.00
## cor(subclusterConc_an:other_contribution_c,subclusterPS:other_contribution_c) 1.00
## cor(subclusterConc_in:other_contribution_c,subclusterPS:other_contribution_c) 1.00
## cor(subclusterEM:other_contribution_c,subclusterPS:other_contribution_c) 1.00
## cor(Intercept,subclusterSS:other_contribution_c) 1.00
## cor(subclusterConc_an,subclusterSS:other_contribution_c) 1.00
## cor(subclusterConc_in,subclusterSS:other_contribution_c) 1.00
## cor(subclusterEM,subclusterSS:other_contribution_c) 1.00
## cor(subclusterPS,subclusterSS:other_contribution_c) 1.00
## cor(subclusterSS,subclusterSS:other_contribution_c) 1.00
## cor(other_contribution_c,subclusterSS:other_contribution_c) 1.00
## cor(subclusterConc_an:other_contribution_c,subclusterSS:other_contribution_c) 1.00
## cor(subclusterConc_in:other_contribution_c,subclusterSS:other_contribution_c) 1.00
## cor(subclusterEM:other_contribution_c,subclusterSS:other_contribution_c) 1.00
## cor(subclusterPS:other_contribution_c,subclusterSS:other_contribution_c) 1.00
## Bulk_ESS
## sd(Intercept) 2202
## sd(subclusterConc_an) 148
## sd(subclusterConc_in) 146
## sd(subclusterEM) 1548
## sd(subclusterPS) 590
## sd(subclusterSS) 1303
## sd(other_contribution_c) 261
## sd(subclusterConc_an:other_contribution_c) 139
## sd(subclusterConc_in:other_contribution_c) 142
## sd(subclusterEM:other_contribution_c) 1375
## sd(subclusterPS:other_contribution_c) 687
## sd(subclusterSS:other_contribution_c) 1468
## cor(Intercept,subclusterConc_an) 429
## cor(Intercept,subclusterConc_in) 911
## cor(subclusterConc_an,subclusterConc_in) 177
## cor(Intercept,subclusterEM) 12310
## cor(subclusterConc_an,subclusterEM) 6739
## cor(subclusterConc_in,subclusterEM) 6052
## cor(Intercept,subclusterPS) 2748
## cor(subclusterConc_an,subclusterPS) 3143
## cor(subclusterConc_in,subclusterPS) 3174
## cor(subclusterEM,subclusterPS) 2351
## cor(Intercept,subclusterSS) 10881
## cor(subclusterConc_an,subclusterSS) 7355
## cor(subclusterConc_in,subclusterSS) 8726
## cor(subclusterEM,subclusterSS) 6000
## cor(subclusterPS,subclusterSS) 7686
## cor(Intercept,other_contribution_c) 3198
## cor(subclusterConc_an,other_contribution_c) 1740
## cor(subclusterConc_in,other_contribution_c) 1183
## cor(subclusterEM,other_contribution_c) 931
## cor(subclusterPS,other_contribution_c) 1131
## cor(subclusterSS,other_contribution_c) 687
## cor(Intercept,subclusterConc_an:other_contribution_c) 3222
## cor(subclusterConc_an,subclusterConc_an:other_contribution_c) 1304
## cor(subclusterConc_in,subclusterConc_an:other_contribution_c) 1974
## cor(subclusterEM,subclusterConc_an:other_contribution_c) 1947
## cor(subclusterPS,subclusterConc_an:other_contribution_c) 2288
## cor(subclusterSS,subclusterConc_an:other_contribution_c) 801
## cor(other_contribution_c,subclusterConc_an:other_contribution_c) 429
## cor(Intercept,subclusterConc_in:other_contribution_c) 2601
## cor(subclusterConc_an,subclusterConc_in:other_contribution_c) 281
## cor(subclusterConc_in,subclusterConc_in:other_contribution_c) 694
## cor(subclusterEM,subclusterConc_in:other_contribution_c) 1924
## cor(subclusterPS,subclusterConc_in:other_contribution_c) 2483
## cor(subclusterSS,subclusterConc_in:other_contribution_c) 847
## cor(other_contribution_c,subclusterConc_in:other_contribution_c) 332
## cor(subclusterConc_an:other_contribution_c,subclusterConc_in:other_contribution_c) 166
## cor(Intercept,subclusterEM:other_contribution_c) 5439
## cor(subclusterConc_an,subclusterEM:other_contribution_c) 3743
## cor(subclusterConc_in,subclusterEM:other_contribution_c) 3401
## cor(subclusterEM,subclusterEM:other_contribution_c) 2021
## cor(subclusterPS,subclusterEM:other_contribution_c) 3222
## cor(subclusterSS,subclusterEM:other_contribution_c) 2698
## cor(other_contribution_c,subclusterEM:other_contribution_c) 1210
## cor(subclusterConc_an:other_contribution_c,subclusterEM:other_contribution_c) 4227
## cor(subclusterConc_in:other_contribution_c,subclusterEM:other_contribution_c) 4025
## cor(Intercept,subclusterPS:other_contribution_c) 4028
## cor(subclusterConc_an,subclusterPS:other_contribution_c) 2037
## cor(subclusterConc_in,subclusterPS:other_contribution_c) 1336
## cor(subclusterEM,subclusterPS:other_contribution_c) 1338
## cor(subclusterPS,subclusterPS:other_contribution_c) 1308
## cor(subclusterSS,subclusterPS:other_contribution_c) 1956
## cor(other_contribution_c,subclusterPS:other_contribution_c) 3603
## cor(subclusterConc_an:other_contribution_c,subclusterPS:other_contribution_c) 2553
## cor(subclusterConc_in:other_contribution_c,subclusterPS:other_contribution_c) 3216
## cor(subclusterEM:other_contribution_c,subclusterPS:other_contribution_c) 4677
## cor(Intercept,subclusterSS:other_contribution_c) 4547
## cor(subclusterConc_an,subclusterSS:other_contribution_c) 1286
## cor(subclusterConc_in,subclusterSS:other_contribution_c) 1443
## cor(subclusterEM,subclusterSS:other_contribution_c) 7037
## cor(subclusterPS,subclusterSS:other_contribution_c) 8321
## cor(subclusterSS,subclusterSS:other_contribution_c) 7729
## cor(other_contribution_c,subclusterSS:other_contribution_c) 2129
## cor(subclusterConc_an:other_contribution_c,subclusterSS:other_contribution_c) 2614
## cor(subclusterConc_in:other_contribution_c,subclusterSS:other_contribution_c) 7762
## cor(subclusterEM:other_contribution_c,subclusterSS:other_contribution_c) 8068
## cor(subclusterPS:other_contribution_c,subclusterSS:other_contribution_c) 6222
## Tail_ESS
## sd(Intercept) 4597
## sd(subclusterConc_an) 774
## sd(subclusterConc_in) 801
## sd(subclusterEM) 2517
## sd(subclusterPS) 1261
## sd(subclusterSS) 4174
## sd(other_contribution_c) 1977
## sd(subclusterConc_an:other_contribution_c) 883
## sd(subclusterConc_in:other_contribution_c) 1011
## sd(subclusterEM:other_contribution_c) 1040
## sd(subclusterPS:other_contribution_c) 1138
## sd(subclusterSS:other_contribution_c) 5117
## cor(Intercept,subclusterConc_an) 1074
## cor(Intercept,subclusterConc_in) 1203
## cor(subclusterConc_an,subclusterConc_in) 762
## cor(Intercept,subclusterEM) 8500
## cor(subclusterConc_an,subclusterEM) 7817
## cor(subclusterConc_in,subclusterEM) 8436
## cor(Intercept,subclusterPS) 4972
## cor(subclusterConc_an,subclusterPS) 4996
## cor(subclusterConc_in,subclusterPS) 4094
## cor(subclusterEM,subclusterPS) 4232
## cor(Intercept,subclusterSS) 7739
## cor(subclusterConc_an,subclusterSS) 7340
## cor(subclusterConc_in,subclusterSS) 8472
## cor(subclusterEM,subclusterSS) 8496
## cor(subclusterPS,subclusterSS) 8694
## cor(Intercept,other_contribution_c) 6449
## cor(subclusterConc_an,other_contribution_c) 2466
## cor(subclusterConc_in,other_contribution_c) 1292
## cor(subclusterEM,other_contribution_c) 2010
## cor(subclusterPS,other_contribution_c) 2037
## cor(subclusterSS,other_contribution_c) 1343
## cor(Intercept,subclusterConc_an:other_contribution_c) 2783
## cor(subclusterConc_an,subclusterConc_an:other_contribution_c) 2792
## cor(subclusterConc_in,subclusterConc_an:other_contribution_c) 2935
## cor(subclusterEM,subclusterConc_an:other_contribution_c) 3426
## cor(subclusterPS,subclusterConc_an:other_contribution_c) 3494
## cor(subclusterSS,subclusterConc_an:other_contribution_c) 3667
## cor(other_contribution_c,subclusterConc_an:other_contribution_c) 1466
## cor(Intercept,subclusterConc_in:other_contribution_c) 2186
## cor(subclusterConc_an,subclusterConc_in:other_contribution_c) 1046
## cor(subclusterConc_in,subclusterConc_in:other_contribution_c) 1477
## cor(subclusterEM,subclusterConc_in:other_contribution_c) 3525
## cor(subclusterPS,subclusterConc_in:other_contribution_c) 3654
## cor(subclusterSS,subclusterConc_in:other_contribution_c) 3399
## cor(other_contribution_c,subclusterConc_in:other_contribution_c) 1473
## cor(subclusterConc_an:other_contribution_c,subclusterConc_in:other_contribution_c) 1270
## cor(Intercept,subclusterEM:other_contribution_c) 8165
## cor(subclusterConc_an,subclusterEM:other_contribution_c) 3837
## cor(subclusterConc_in,subclusterEM:other_contribution_c) 4802
## cor(subclusterEM,subclusterEM:other_contribution_c) 5214
## cor(subclusterPS,subclusterEM:other_contribution_c) 5162
## cor(subclusterSS,subclusterEM:other_contribution_c) 4915
## cor(other_contribution_c,subclusterEM:other_contribution_c) 5830
## cor(subclusterConc_an:other_contribution_c,subclusterEM:other_contribution_c) 6581
## cor(subclusterConc_in:other_contribution_c,subclusterEM:other_contribution_c) 6076
## cor(Intercept,subclusterPS:other_contribution_c) 4368
## cor(subclusterConc_an,subclusterPS:other_contribution_c) 2462
## cor(subclusterConc_in,subclusterPS:other_contribution_c) 1959
## cor(subclusterEM,subclusterPS:other_contribution_c) 2697
## cor(subclusterPS,subclusterPS:other_contribution_c) 1831
## cor(subclusterSS,subclusterPS:other_contribution_c) 4307
## cor(other_contribution_c,subclusterPS:other_contribution_c) 6567
## cor(subclusterConc_an:other_contribution_c,subclusterPS:other_contribution_c) 3001
## cor(subclusterConc_in:other_contribution_c,subclusterPS:other_contribution_c) 2901
## cor(subclusterEM:other_contribution_c,subclusterPS:other_contribution_c) 7174
## cor(Intercept,subclusterSS:other_contribution_c) 6790
## cor(subclusterConc_an,subclusterSS:other_contribution_c) 6208
## cor(subclusterConc_in,subclusterSS:other_contribution_c) 6786
## cor(subclusterEM,subclusterSS:other_contribution_c) 9259
## cor(subclusterPS,subclusterSS:other_contribution_c) 9707
## cor(subclusterSS,subclusterSS:other_contribution_c) 8821
## cor(other_contribution_c,subclusterSS:other_contribution_c) 8416
## cor(subclusterConc_an:other_contribution_c,subclusterSS:other_contribution_c) 8839
## cor(subclusterConc_in:other_contribution_c,subclusterSS:other_contribution_c) 9620
## cor(subclusterEM:other_contribution_c,subclusterSS:other_contribution_c) 9216
## cor(subclusterPS:other_contribution_c,subclusterSS:other_contribution_c) 7945
##
## ~word (Number of levels: 32)
## Estimate Est.Error l-95% CI u-95% CI Rhat
## sd(Intercept) 0.04 0.02 0.00 0.09 1.00
## sd(other_contribution_c) 0.00 0.00 0.00 0.01 1.00
## cor(Intercept,other_contribution_c) 0.06 0.55 -0.93 0.95 1.00
## Bulk_ESS Tail_ESS
## sd(Intercept) 2717 4398
## sd(other_contribution_c) 2502 3311
## cor(Intercept,other_contribution_c) 3500 6403
##
## Population-Level Effects:
## Estimate Est.Error l-95% CI u-95% CI
## Intercept 0.98 0.09 0.81 1.16
## phi_Intercept 3.73 0.07 3.58 3.87
## subclusterConc_an -0.02 0.07 -0.16 0.12
## subclusterConc_in -0.05 0.06 -0.17 0.08
## subclusterEM -0.05 0.06 -0.17 0.07
## subclusterPS -0.01 0.07 -0.15 0.14
## subclusterSS -0.08 0.07 -0.22 0.05
## other_contribution_c 0.02 0.00 0.01 0.03
## difficulty_c -0.01 0.00 -0.01 -0.00
## subclusterConc_an:other_contribution_c -0.00 0.00 -0.01 0.01
## subclusterConc_in:other_contribution_c -0.00 0.00 -0.01 0.01
## subclusterEM:other_contribution_c -0.00 0.00 -0.01 0.00
## subclusterPS:other_contribution_c -0.00 0.00 -0.01 0.00
## subclusterSS:other_contribution_c -0.00 0.00 -0.01 0.00
## Rhat Bulk_ESS Tail_ESS
## Intercept 1.00 1166 3455
## phi_Intercept 1.00 2255 5580
## subclusterConc_an 1.00 3903 6017
## subclusterConc_in 1.00 4716 6286
## subclusterEM 1.00 6072 7471
## subclusterPS 1.00 4358 6471
## subclusterSS 1.00 6631 7261
## other_contribution_c 1.00 1793 5343
## difficulty_c 1.00 11061 10894
## subclusterConc_an:other_contribution_c 1.00 3372 6252
## subclusterConc_in:other_contribution_c 1.00 1923 5854
## subclusterEM:other_contribution_c 1.00 5995 8197
## subclusterPS:other_contribution_c 1.00 5357 6614
## subclusterSS:other_contribution_c 1.00 6524 7835
##
## Draws were sampled using sampling(NUTS). For each parameter, Bulk_ESS
## and Tail_ESS are effective sample size measures, and Rhat is the potential
## scale reduction factor on split chains (at convergence, Rhat = 1).Perform hypothesis tests on the fixed effects coefficient:
hypothesis(subcluster_dist_mdl,
'difficulty_c < 0')## Hypothesis Tests for class b:
## Hypothesis Estimate Est.Error CI.Lower CI.Upper Evid.Ratio Post.Prob
## 1 (difficulty_c) < 0 -0.01 0 -0.01 0 Inf 1
## Star
## 1 *
## ---
## 'CI': 90%-CI for one-sided and 95%-CI for two-sided hypotheses.
## '*': For one-sided hypotheses, the posterior probability exceeds 95%;
## for two-sided hypotheses, the value tested against lies outside the 95%-CI.
## Posterior probabilities of point hypotheses assume equal prior probabilities.hypothesis(subcluster_dist_mdl,
'other_contribution_c > 0')## Hypothesis Tests for class b:
## Hypothesis Estimate Est.Error CI.Lower CI.Upper Evid.Ratio
## 1 (other_contributi... > 0 0.02 0 0.01 0.03 Inf
## Post.Prob Star
## 1 1 *
## ---
## 'CI': 90%-CI for one-sided and 95%-CI for two-sided hypotheses.
## '*': For one-sided hypotheses, the posterior probability exceeds 95%;
## for two-sided hypotheses, the value tested against lies outside the 95%-CI.
## Posterior probabilities of point hypotheses assume equal prior probabilities.hypothesis(subcluster_dist_mdl,
'subclusterConc_an:other_contribution_c < 0') # PSTQ is reference## Hypothesis Tests for class b:
## Hypothesis Estimate Est.Error CI.Lower CI.Upper Evid.Ratio
## 1 (subclusterConc_a... < 0 0 0 -0.01 0 2.07
## Post.Prob Star
## 1 0.67
## ---
## 'CI': 90%-CI for one-sided and 95%-CI for two-sided hypotheses.
## '*': For one-sided hypotheses, the posterior probability exceeds 95%;
## for two-sided hypotheses, the value tested against lies outside the 95%-CI.
## Posterior probabilities of point hypotheses assume equal prior probabilities.hypothesis(subcluster_dist_mdl,
'subclusterConc_in:other_contribution_c < 0') # PSTQ is reference## Hypothesis Tests for class b:
## Hypothesis Estimate Est.Error CI.Lower CI.Upper Evid.Ratio
## 1 (subclusterConc_i... < 0 0 0 -0.01 0 1.84
## Post.Prob Star
## 1 0.65
## ---
## 'CI': 90%-CI for one-sided and 95%-CI for two-sided hypotheses.
## '*': For one-sided hypotheses, the posterior probability exceeds 95%;
## for two-sided hypotheses, the value tested against lies outside the 95%-CI.
## Posterior probabilities of point hypotheses assume equal prior probabilities.hypothesis(subcluster_dist_mdl,
'subclusterEM:other_contribution_c < 0') # PSTQ is reference## Hypothesis Tests for class b:
## Hypothesis Estimate Est.Error CI.Lower CI.Upper Evid.Ratio
## 1 (subclusterEM:oth... < 0 0 0 -0.01 0 4.6
## Post.Prob Star
## 1 0.82
## ---
## 'CI': 90%-CI for one-sided and 95%-CI for two-sided hypotheses.
## '*': For one-sided hypotheses, the posterior probability exceeds 95%;
## for two-sided hypotheses, the value tested against lies outside the 95%-CI.
## Posterior probabilities of point hypotheses assume equal prior probabilities.hypothesis(subcluster_dist_mdl,
'subclusterPS:other_contribution_c < 0') # PSTQ is reference## Hypothesis Tests for class b:
## Hypothesis Estimate Est.Error CI.Lower CI.Upper Evid.Ratio
## 1 (subclusterPS:oth... < 0 0 0 -0.01 0 5.52
## Post.Prob Star
## 1 0.85
## ---
## 'CI': 90%-CI for one-sided and 95%-CI for two-sided hypotheses.
## '*': For one-sided hypotheses, the posterior probability exceeds 95%;
## for two-sided hypotheses, the value tested against lies outside the 95%-CI.
## Posterior probabilities of point hypotheses assume equal prior probabilities.hypothesis(subcluster_dist_mdl,
'subclusterSS:other_contribution_c < 0') # PSTQ is reference## Hypothesis Tests for class b:
## Hypothesis Estimate Est.Error CI.Lower CI.Upper Evid.Ratio
## 1 (subclusterSS:oth... < 0 0 0 -0.01 0 6.88
## Post.Prob Star
## 1 0.87
## ---
## 'CI': 90%-CI for one-sided and 95%-CI for two-sided hypotheses.
## '*': For one-sided hypotheses, the posterior probability exceeds 95%;
## for two-sided hypotheses, the value tested against lies outside the 95%-CI.
## Posterior probabilities of point hypotheses assume equal prior probabilities.14 Subcluster models: self-contribution
Do the main analysis of IOS with difficulty
as a covariate predictor, to control for this.
subcluster_self_mdl <- brm(IOS ~
# Fixed effects:
1 +
subcluster +
self_contribution_c +
difficulty_c +
subcluster:self_contribution_c +
# Random effects:
(1 +
subcluster +
self_contribution_c +
subcluster:self_contribution_c|participant) +
(1 + self_contribution_c|word),
data = df,
family = cumulative,
# MCMC settings:
seed = 42,
cores = 4,
iter = 6000,
warmup = 3000,
control = list(adapt_delta = 0.99))
# Save model:
save(subcluster_self_mdl,
file = '../models_E2/subcluster_self_mdl.Rdata')Load model:
load('../models_E2/subcluster_self_mdl.RData')Show priors:
prior_summary(subcluster_self_mdl)## prior class coef
## (flat) b
## (flat) b difficulty_c
## (flat) b self_contribution_c
## (flat) b subclusterConc_an
## (flat) b subclusterConc_an:self_contribution_c
## (flat) b subclusterConc_in
## (flat) b subclusterConc_in:self_contribution_c
## (flat) b subclusterEM
## (flat) b subclusterEM:self_contribution_c
## (flat) b subclusterPS
## (flat) b subclusterPS:self_contribution_c
## (flat) b subclusterSS
## (flat) b subclusterSS:self_contribution_c
## student_t(3, 0, 2.5) Intercept
## student_t(3, 0, 2.5) Intercept 1
## student_t(3, 0, 2.5) Intercept 2
## student_t(3, 0, 2.5) Intercept 3
## student_t(3, 0, 2.5) Intercept 4
## student_t(3, 0, 2.5) Intercept 5
## lkj_corr_cholesky(1) L
## lkj_corr_cholesky(1) L
## lkj_corr_cholesky(1) L
## student_t(3, 0, 2.5) sd
## student_t(3, 0, 2.5) sd
## student_t(3, 0, 2.5) sd Intercept
## student_t(3, 0, 2.5) sd self_contribution_c
## student_t(3, 0, 2.5) sd subclusterConc_an
## student_t(3, 0, 2.5) sd subclusterConc_an:self_contribution_c
## student_t(3, 0, 2.5) sd subclusterConc_in
## student_t(3, 0, 2.5) sd subclusterConc_in:self_contribution_c
## student_t(3, 0, 2.5) sd subclusterEM
## student_t(3, 0, 2.5) sd subclusterEM:self_contribution_c
## student_t(3, 0, 2.5) sd subclusterPS
## student_t(3, 0, 2.5) sd subclusterPS:self_contribution_c
## student_t(3, 0, 2.5) sd subclusterSS
## student_t(3, 0, 2.5) sd subclusterSS:self_contribution_c
## student_t(3, 0, 2.5) sd
## student_t(3, 0, 2.5) sd Intercept
## student_t(3, 0, 2.5) sd self_contribution_c
## group resp dpar nlpar lb ub source
## default
## (vectorized)
## (vectorized)
## (vectorized)
## (vectorized)
## (vectorized)
## (vectorized)
## (vectorized)
## (vectorized)
## (vectorized)
## (vectorized)
## (vectorized)
## (vectorized)
## default
## (vectorized)
## (vectorized)
## (vectorized)
## (vectorized)
## (vectorized)
## default
## participant (vectorized)
## word (vectorized)
## 0 default
## participant 0 (vectorized)
## participant 0 (vectorized)
## participant 0 (vectorized)
## participant 0 (vectorized)
## participant 0 (vectorized)
## participant 0 (vectorized)
## participant 0 (vectorized)
## participant 0 (vectorized)
## participant 0 (vectorized)
## participant 0 (vectorized)
## participant 0 (vectorized)
## participant 0 (vectorized)
## participant 0 (vectorized)
## word 0 (vectorized)
## word 0 (vectorized)
## word 0 (vectorized)Check posterior predictive checks of the mixed beta regression:
pp_check(subcluster_self_mdl, ndraws = 100)
Check this model:
subcluster_self_mdl## Family: cumulative
## Links: mu = logit; disc = identity
## Formula: IOS ~ 1 + subcluster + self_contribution_c + difficulty_c + subcluster:self_contribution_c + (1 + subcluster + self_contribution_c + subcluster:self_contribution_c | participant) + (1 + self_contribution_c | word)
## Data: df (Number of observations: 1032)
## Draws: 4 chains, each with iter = 6000; warmup = 3000; thin = 1;
## total post-warmup draws = 12000
##
## Group-Level Effects:
## ~participant (Number of levels: 129)
## Estimate
## sd(Intercept) 2.90
## sd(subclusterConc_an) 1.71
## sd(subclusterConc_in) 1.94
## sd(subclusterEM) 0.45
## sd(subclusterPS) 1.03
## sd(subclusterSS) 0.49
## sd(self_contribution_c) 0.06
## sd(subclusterConc_an:self_contribution_c) 0.03
## sd(subclusterConc_in:self_contribution_c) 0.03
## sd(subclusterEM:self_contribution_c) 0.04
## sd(subclusterPS:self_contribution_c) 0.03
## sd(subclusterSS:self_contribution_c) 0.04
## cor(Intercept,subclusterConc_an) -0.18
## cor(Intercept,subclusterConc_in) -0.16
## cor(subclusterConc_an,subclusterConc_in) 0.78
## cor(Intercept,subclusterEM) 0.00
## cor(subclusterConc_an,subclusterEM) -0.05
## cor(subclusterConc_in,subclusterEM) -0.07
## cor(Intercept,subclusterPS) 0.00
## cor(subclusterConc_an,subclusterPS) -0.23
## cor(subclusterConc_in,subclusterPS) -0.24
## cor(subclusterEM,subclusterPS) 0.06
## cor(Intercept,subclusterSS) 0.03
## cor(subclusterConc_an,subclusterSS) -0.02
## cor(subclusterConc_in,subclusterSS) 0.00
## cor(subclusterEM,subclusterSS) 0.02
## cor(subclusterPS,subclusterSS) 0.05
## cor(Intercept,self_contribution_c) 0.19
## cor(subclusterConc_an,self_contribution_c) -0.13
## cor(subclusterConc_in,self_contribution_c) -0.17
## cor(subclusterEM,self_contribution_c) -0.02
## cor(subclusterPS,self_contribution_c) 0.24
## cor(subclusterSS,self_contribution_c) 0.08
## cor(Intercept,subclusterConc_an:self_contribution_c) 0.10
## cor(subclusterConc_an,subclusterConc_an:self_contribution_c) 0.04
## cor(subclusterConc_in,subclusterConc_an:self_contribution_c) 0.00
## cor(subclusterEM,subclusterConc_an:self_contribution_c) 0.00
## cor(subclusterPS,subclusterConc_an:self_contribution_c) 0.03
## cor(subclusterSS,subclusterConc_an:self_contribution_c) 0.01
## cor(self_contribution_c,subclusterConc_an:self_contribution_c) 0.16
## cor(Intercept,subclusterConc_in:self_contribution_c) 0.06
## cor(subclusterConc_an,subclusterConc_in:self_contribution_c) 0.08
## cor(subclusterConc_in,subclusterConc_in:self_contribution_c) 0.13
## cor(subclusterEM,subclusterConc_in:self_contribution_c) -0.07
## cor(subclusterPS,subclusterConc_in:self_contribution_c) 0.09
## cor(subclusterSS,subclusterConc_in:self_contribution_c) 0.01
## cor(self_contribution_c,subclusterConc_in:self_contribution_c) -0.03
## cor(subclusterConc_an:self_contribution_c,subclusterConc_in:self_contribution_c) 0.15
## cor(Intercept,subclusterEM:self_contribution_c) 0.04
## cor(subclusterConc_an,subclusterEM:self_contribution_c) -0.01
## cor(subclusterConc_in,subclusterEM:self_contribution_c) -0.04
## cor(subclusterEM,subclusterEM:self_contribution_c) 0.05
## cor(subclusterPS,subclusterEM:self_contribution_c) -0.13
## cor(subclusterSS,subclusterEM:self_contribution_c) 0.01
## cor(self_contribution_c,subclusterEM:self_contribution_c) -0.24
## cor(subclusterConc_an:self_contribution_c,subclusterEM:self_contribution_c) -0.01
## cor(subclusterConc_in:self_contribution_c,subclusterEM:self_contribution_c) -0.08
## cor(Intercept,subclusterPS:self_contribution_c) 0.02
## cor(subclusterConc_an,subclusterPS:self_contribution_c) -0.03
## cor(subclusterConc_in,subclusterPS:self_contribution_c) 0.02
## cor(subclusterEM,subclusterPS:self_contribution_c) -0.03
## cor(subclusterPS,subclusterPS:self_contribution_c) 0.04
## cor(subclusterSS,subclusterPS:self_contribution_c) 0.00
## cor(self_contribution_c,subclusterPS:self_contribution_c) 0.02
## cor(subclusterConc_an:self_contribution_c,subclusterPS:self_contribution_c) -0.01
## cor(subclusterConc_in:self_contribution_c,subclusterPS:self_contribution_c) 0.03
## cor(subclusterEM:self_contribution_c,subclusterPS:self_contribution_c) 0.01
## cor(Intercept,subclusterSS:self_contribution_c) 0.02
## cor(subclusterConc_an,subclusterSS:self_contribution_c) -0.08
## cor(subclusterConc_in,subclusterSS:self_contribution_c) -0.14
## cor(subclusterEM,subclusterSS:self_contribution_c) 0.02
## cor(subclusterPS,subclusterSS:self_contribution_c) 0.01
## cor(subclusterSS,subclusterSS:self_contribution_c) -0.03
## cor(self_contribution_c,subclusterSS:self_contribution_c) -0.02
## cor(subclusterConc_an:self_contribution_c,subclusterSS:self_contribution_c) -0.00
## cor(subclusterConc_in:self_contribution_c,subclusterSS:self_contribution_c) -0.05
## cor(subclusterEM:self_contribution_c,subclusterSS:self_contribution_c) 0.02
## cor(subclusterPS:self_contribution_c,subclusterSS:self_contribution_c) 0.01
## Est.Error
## sd(Intercept) 0.27
## sd(subclusterConc_an) 0.31
## sd(subclusterConc_in) 0.30
## sd(subclusterEM) 0.33
## sd(subclusterPS) 0.47
## sd(subclusterSS) 0.37
## sd(self_contribution_c) 0.01
## sd(subclusterConc_an:self_contribution_c) 0.02
## sd(subclusterConc_in:self_contribution_c) 0.02
## sd(subclusterEM:self_contribution_c) 0.02
## sd(subclusterPS:self_contribution_c) 0.02
## sd(subclusterSS:self_contribution_c) 0.03
## cor(Intercept,subclusterConc_an) 0.14
## cor(Intercept,subclusterConc_in) 0.13
## cor(subclusterConc_an,subclusterConc_in) 0.09
## cor(Intercept,subclusterEM) 0.26
## cor(subclusterConc_an,subclusterEM) 0.27
## cor(subclusterConc_in,subclusterEM) 0.26
## cor(Intercept,subclusterPS) 0.21
## cor(subclusterConc_an,subclusterPS) 0.22
## cor(subclusterConc_in,subclusterPS) 0.22
## cor(subclusterEM,subclusterPS) 0.27
## cor(Intercept,subclusterSS) 0.26
## cor(subclusterConc_an,subclusterSS) 0.26
## cor(subclusterConc_in,subclusterSS) 0.26
## cor(subclusterEM,subclusterSS) 0.28
## cor(subclusterPS,subclusterSS) 0.28
## cor(Intercept,self_contribution_c) 0.16
## cor(subclusterConc_an,self_contribution_c) 0.19
## cor(subclusterConc_in,self_contribution_c) 0.18
## cor(subclusterEM,self_contribution_c) 0.27
## cor(subclusterPS,self_contribution_c) 0.24
## cor(subclusterSS,self_contribution_c) 0.27
## cor(Intercept,subclusterConc_an:self_contribution_c) 0.24
## cor(subclusterConc_an,subclusterConc_an:self_contribution_c) 0.24
## cor(subclusterConc_in,subclusterConc_an:self_contribution_c) 0.24
## cor(subclusterEM,subclusterConc_an:self_contribution_c) 0.28
## cor(subclusterPS,subclusterConc_an:self_contribution_c) 0.27
## cor(subclusterSS,subclusterConc_an:self_contribution_c) 0.28
## cor(self_contribution_c,subclusterConc_an:self_contribution_c) 0.26
## cor(Intercept,subclusterConc_in:self_contribution_c) 0.24
## cor(subclusterConc_an,subclusterConc_in:self_contribution_c) 0.25
## cor(subclusterConc_in,subclusterConc_in:self_contribution_c) 0.25
## cor(subclusterEM,subclusterConc_in:self_contribution_c) 0.28
## cor(subclusterPS,subclusterConc_in:self_contribution_c) 0.27
## cor(subclusterSS,subclusterConc_in:self_contribution_c) 0.28
## cor(self_contribution_c,subclusterConc_in:self_contribution_c) 0.26
## cor(subclusterConc_an:self_contribution_c,subclusterConc_in:self_contribution_c) 0.29
## cor(Intercept,subclusterEM:self_contribution_c) 0.24
## cor(subclusterConc_an,subclusterEM:self_contribution_c) 0.24
## cor(subclusterConc_in,subclusterEM:self_contribution_c) 0.24
## cor(subclusterEM,subclusterEM:self_contribution_c) 0.27
## cor(subclusterPS,subclusterEM:self_contribution_c) 0.27
## cor(subclusterSS,subclusterEM:self_contribution_c) 0.28
## cor(self_contribution_c,subclusterEM:self_contribution_c) 0.27
## cor(subclusterConc_an:self_contribution_c,subclusterEM:self_contribution_c) 0.27
## cor(subclusterConc_in:self_contribution_c,subclusterEM:self_contribution_c) 0.27
## cor(Intercept,subclusterPS:self_contribution_c) 0.25
## cor(subclusterConc_an,subclusterPS:self_contribution_c) 0.26
## cor(subclusterConc_in,subclusterPS:self_contribution_c) 0.26
## cor(subclusterEM,subclusterPS:self_contribution_c) 0.28
## cor(subclusterPS,subclusterPS:self_contribution_c) 0.27
## cor(subclusterSS,subclusterPS:self_contribution_c) 0.28
## cor(self_contribution_c,subclusterPS:self_contribution_c) 0.27
## cor(subclusterConc_an:self_contribution_c,subclusterPS:self_contribution_c) 0.27
## cor(subclusterConc_in:self_contribution_c,subclusterPS:self_contribution_c) 0.28
## cor(subclusterEM:self_contribution_c,subclusterPS:self_contribution_c) 0.27
## cor(Intercept,subclusterSS:self_contribution_c) 0.23
## cor(subclusterConc_an,subclusterSS:self_contribution_c) 0.25
## cor(subclusterConc_in,subclusterSS:self_contribution_c) 0.25
## cor(subclusterEM,subclusterSS:self_contribution_c) 0.28
## cor(subclusterPS,subclusterSS:self_contribution_c) 0.27
## cor(subclusterSS,subclusterSS:self_contribution_c) 0.28
## cor(self_contribution_c,subclusterSS:self_contribution_c) 0.27
## cor(subclusterConc_an:self_contribution_c,subclusterSS:self_contribution_c) 0.27
## cor(subclusterConc_in:self_contribution_c,subclusterSS:self_contribution_c) 0.27
## cor(subclusterEM:self_contribution_c,subclusterSS:self_contribution_c) 0.27
## cor(subclusterPS:self_contribution_c,subclusterSS:self_contribution_c) 0.28
## l-95% CI
## sd(Intercept) 2.40
## sd(subclusterConc_an) 1.11
## sd(subclusterConc_in) 1.36
## sd(subclusterEM) 0.02
## sd(subclusterPS) 0.10
## sd(subclusterSS) 0.02
## sd(self_contribution_c) 0.03
## sd(subclusterConc_an:self_contribution_c) 0.00
## sd(subclusterConc_in:self_contribution_c) 0.00
## sd(subclusterEM:self_contribution_c) 0.00
## sd(subclusterPS:self_contribution_c) 0.00
## sd(subclusterSS:self_contribution_c) 0.00
## cor(Intercept,subclusterConc_an) -0.44
## cor(Intercept,subclusterConc_in) -0.40
## cor(subclusterConc_an,subclusterConc_in) 0.57
## cor(Intercept,subclusterEM) -0.49
## cor(subclusterConc_an,subclusterEM) -0.56
## cor(subclusterConc_in,subclusterEM) -0.57
## cor(Intercept,subclusterPS) -0.39
## cor(subclusterConc_an,subclusterPS) -0.64
## cor(subclusterConc_in,subclusterPS) -0.63
## cor(subclusterEM,subclusterPS) -0.47
## cor(Intercept,subclusterSS) -0.47
## cor(subclusterConc_an,subclusterSS) -0.53
## cor(subclusterConc_in,subclusterSS) -0.51
## cor(subclusterEM,subclusterSS) -0.52
## cor(subclusterPS,subclusterSS) -0.50
## cor(Intercept,self_contribution_c) -0.13
## cor(subclusterConc_an,self_contribution_c) -0.49
## cor(subclusterConc_in,self_contribution_c) -0.51
## cor(subclusterEM,self_contribution_c) -0.52
## cor(subclusterPS,self_contribution_c) -0.27
## cor(subclusterSS,self_contribution_c) -0.47
## cor(Intercept,subclusterConc_an:self_contribution_c) -0.39
## cor(subclusterConc_an,subclusterConc_an:self_contribution_c) -0.45
## cor(subclusterConc_in,subclusterConc_an:self_contribution_c) -0.47
## cor(subclusterEM,subclusterConc_an:self_contribution_c) -0.53
## cor(subclusterPS,subclusterConc_an:self_contribution_c) -0.49
## cor(subclusterSS,subclusterConc_an:self_contribution_c) -0.52
## cor(self_contribution_c,subclusterConc_an:self_contribution_c) -0.39
## cor(Intercept,subclusterConc_in:self_contribution_c) -0.42
## cor(subclusterConc_an,subclusterConc_in:self_contribution_c) -0.41
## cor(subclusterConc_in,subclusterConc_in:self_contribution_c) -0.37
## cor(subclusterEM,subclusterConc_in:self_contribution_c) -0.58
## cor(subclusterPS,subclusterConc_in:self_contribution_c) -0.45
## cor(subclusterSS,subclusterConc_in:self_contribution_c) -0.53
## cor(self_contribution_c,subclusterConc_in:self_contribution_c) -0.52
## cor(subclusterConc_an:self_contribution_c,subclusterConc_in:self_contribution_c) -0.45
## cor(Intercept,subclusterEM:self_contribution_c) -0.44
## cor(subclusterConc_an,subclusterEM:self_contribution_c) -0.49
## cor(subclusterConc_in,subclusterEM:self_contribution_c) -0.49
## cor(subclusterEM,subclusterEM:self_contribution_c) -0.48
## cor(subclusterPS,subclusterEM:self_contribution_c) -0.62
## cor(subclusterSS,subclusterEM:self_contribution_c) -0.53
## cor(self_contribution_c,subclusterEM:self_contribution_c) -0.70
## cor(subclusterConc_an:self_contribution_c,subclusterEM:self_contribution_c) -0.53
## cor(subclusterConc_in:self_contribution_c,subclusterEM:self_contribution_c) -0.59
## cor(Intercept,subclusterPS:self_contribution_c) -0.48
## cor(subclusterConc_an,subclusterPS:self_contribution_c) -0.52
## cor(subclusterConc_in,subclusterPS:self_contribution_c) -0.50
## cor(subclusterEM,subclusterPS:self_contribution_c) -0.56
## cor(subclusterPS,subclusterPS:self_contribution_c) -0.49
## cor(subclusterSS,subclusterPS:self_contribution_c) -0.53
## cor(self_contribution_c,subclusterPS:self_contribution_c) -0.51
## cor(subclusterConc_an:self_contribution_c,subclusterPS:self_contribution_c) -0.53
## cor(subclusterConc_in:self_contribution_c,subclusterPS:self_contribution_c) -0.51
## cor(subclusterEM:self_contribution_c,subclusterPS:self_contribution_c) -0.51
## cor(Intercept,subclusterSS:self_contribution_c) -0.44
## cor(subclusterConc_an,subclusterSS:self_contribution_c) -0.55
## cor(subclusterConc_in,subclusterSS:self_contribution_c) -0.59
## cor(subclusterEM,subclusterSS:self_contribution_c) -0.51
## cor(subclusterPS,subclusterSS:self_contribution_c) -0.52
## cor(subclusterSS,subclusterSS:self_contribution_c) -0.55
## cor(self_contribution_c,subclusterSS:self_contribution_c) -0.52
## cor(subclusterConc_an:self_contribution_c,subclusterSS:self_contribution_c) -0.53
## cor(subclusterConc_in:self_contribution_c,subclusterSS:self_contribution_c) -0.56
## cor(subclusterEM:self_contribution_c,subclusterSS:self_contribution_c) -0.50
## cor(subclusterPS:self_contribution_c,subclusterSS:self_contribution_c) -0.51
## u-95% CI
## sd(Intercept) 3.46
## sd(subclusterConc_an) 2.30
## sd(subclusterConc_in) 2.54
## sd(subclusterEM) 1.21
## sd(subclusterPS) 1.93
## sd(subclusterSS) 1.35
## sd(self_contribution_c) 0.08
## sd(subclusterConc_an:self_contribution_c) 0.08
## sd(subclusterConc_in:self_contribution_c) 0.07
## sd(subclusterEM:self_contribution_c) 0.08
## sd(subclusterPS:self_contribution_c) 0.08
## sd(subclusterSS:self_contribution_c) 0.10
## cor(Intercept,subclusterConc_an) 0.10
## cor(Intercept,subclusterConc_in) 0.10
## cor(subclusterConc_an,subclusterConc_in) 0.92
## cor(Intercept,subclusterEM) 0.49
## cor(subclusterConc_an,subclusterEM) 0.47
## cor(subclusterConc_in,subclusterEM) 0.45
## cor(Intercept,subclusterPS) 0.42
## cor(subclusterConc_an,subclusterPS) 0.24
## cor(subclusterConc_in,subclusterPS) 0.21
## cor(subclusterEM,subclusterPS) 0.57
## cor(Intercept,subclusterSS) 0.52
## cor(subclusterConc_an,subclusterSS) 0.49
## cor(subclusterConc_in,subclusterSS) 0.51
## cor(subclusterEM,subclusterSS) 0.55
## cor(subclusterPS,subclusterSS) 0.57
## cor(Intercept,self_contribution_c) 0.49
## cor(subclusterConc_an,self_contribution_c) 0.25
## cor(subclusterConc_in,self_contribution_c) 0.19
## cor(subclusterEM,self_contribution_c) 0.50
## cor(subclusterPS,self_contribution_c) 0.65
## cor(subclusterSS,self_contribution_c) 0.58
## cor(Intercept,subclusterConc_an:self_contribution_c) 0.55
## cor(subclusterConc_an,subclusterConc_an:self_contribution_c) 0.50
## cor(subclusterConc_in,subclusterConc_an:self_contribution_c) 0.48
## cor(subclusterEM,subclusterConc_an:self_contribution_c) 0.54
## cor(subclusterPS,subclusterConc_an:self_contribution_c) 0.54
## cor(subclusterSS,subclusterConc_an:self_contribution_c) 0.55
## cor(self_contribution_c,subclusterConc_an:self_contribution_c) 0.63
## cor(Intercept,subclusterConc_in:self_contribution_c) 0.51
## cor(subclusterConc_an,subclusterConc_in:self_contribution_c) 0.55
## cor(subclusterConc_in,subclusterConc_in:self_contribution_c) 0.58
## cor(subclusterEM,subclusterConc_in:self_contribution_c) 0.49
## cor(subclusterPS,subclusterConc_in:self_contribution_c) 0.58
## cor(subclusterSS,subclusterConc_in:self_contribution_c) 0.55
## cor(self_contribution_c,subclusterConc_in:self_contribution_c) 0.49
## cor(subclusterConc_an:self_contribution_c,subclusterConc_in:self_contribution_c) 0.68
## cor(Intercept,subclusterEM:self_contribution_c) 0.49
## cor(subclusterConc_an,subclusterEM:self_contribution_c) 0.47
## cor(subclusterConc_in,subclusterEM:self_contribution_c) 0.44
## cor(subclusterEM,subclusterEM:self_contribution_c) 0.56
## cor(subclusterPS,subclusterEM:self_contribution_c) 0.42
## cor(subclusterSS,subclusterEM:self_contribution_c) 0.54
## cor(self_contribution_c,subclusterEM:self_contribution_c) 0.35
## cor(subclusterConc_an:self_contribution_c,subclusterEM:self_contribution_c) 0.51
## cor(subclusterConc_in:self_contribution_c,subclusterEM:self_contribution_c) 0.46
## cor(Intercept,subclusterPS:self_contribution_c) 0.50
## cor(subclusterConc_an,subclusterPS:self_contribution_c) 0.48
## cor(subclusterConc_in,subclusterPS:self_contribution_c) 0.51
## cor(subclusterEM,subclusterPS:self_contribution_c) 0.51
## cor(subclusterPS,subclusterPS:self_contribution_c) 0.56
## cor(subclusterSS,subclusterPS:self_contribution_c) 0.53
## cor(self_contribution_c,subclusterPS:self_contribution_c) 0.54
## cor(subclusterConc_an:self_contribution_c,subclusterPS:self_contribution_c) 0.51
## cor(subclusterConc_in:self_contribution_c,subclusterPS:self_contribution_c) 0.56
## cor(subclusterEM:self_contribution_c,subclusterPS:self_contribution_c) 0.53
## cor(Intercept,subclusterSS:self_contribution_c) 0.48
## cor(subclusterConc_an,subclusterSS:self_contribution_c) 0.42
## cor(subclusterConc_in,subclusterSS:self_contribution_c) 0.38
## cor(subclusterEM,subclusterSS:self_contribution_c) 0.55
## cor(subclusterPS,subclusterSS:self_contribution_c) 0.53
## cor(subclusterSS,subclusterSS:self_contribution_c) 0.51
## cor(self_contribution_c,subclusterSS:self_contribution_c) 0.51
## cor(subclusterConc_an:self_contribution_c,subclusterSS:self_contribution_c) 0.53
## cor(subclusterConc_in:self_contribution_c,subclusterSS:self_contribution_c) 0.49
## cor(subclusterEM:self_contribution_c,subclusterSS:self_contribution_c) 0.54
## cor(subclusterPS:self_contribution_c,subclusterSS:self_contribution_c) 0.54
## Rhat
## sd(Intercept) 1.00
## sd(subclusterConc_an) 1.00
## sd(subclusterConc_in) 1.00
## sd(subclusterEM) 1.00
## sd(subclusterPS) 1.00
## sd(subclusterSS) 1.00
## sd(self_contribution_c) 1.00
## sd(subclusterConc_an:self_contribution_c) 1.00
## sd(subclusterConc_in:self_contribution_c) 1.00
## sd(subclusterEM:self_contribution_c) 1.00
## sd(subclusterPS:self_contribution_c) 1.00
## sd(subclusterSS:self_contribution_c) 1.00
## cor(Intercept,subclusterConc_an) 1.00
## cor(Intercept,subclusterConc_in) 1.00
## cor(subclusterConc_an,subclusterConc_in) 1.00
## cor(Intercept,subclusterEM) 1.00
## cor(subclusterConc_an,subclusterEM) 1.00
## cor(subclusterConc_in,subclusterEM) 1.00
## cor(Intercept,subclusterPS) 1.00
## cor(subclusterConc_an,subclusterPS) 1.00
## cor(subclusterConc_in,subclusterPS) 1.00
## cor(subclusterEM,subclusterPS) 1.00
## cor(Intercept,subclusterSS) 1.00
## cor(subclusterConc_an,subclusterSS) 1.00
## cor(subclusterConc_in,subclusterSS) 1.00
## cor(subclusterEM,subclusterSS) 1.00
## cor(subclusterPS,subclusterSS) 1.00
## cor(Intercept,self_contribution_c) 1.00
## cor(subclusterConc_an,self_contribution_c) 1.00
## cor(subclusterConc_in,self_contribution_c) 1.00
## cor(subclusterEM,self_contribution_c) 1.00
## cor(subclusterPS,self_contribution_c) 1.00
## cor(subclusterSS,self_contribution_c) 1.00
## cor(Intercept,subclusterConc_an:self_contribution_c) 1.00
## cor(subclusterConc_an,subclusterConc_an:self_contribution_c) 1.00
## cor(subclusterConc_in,subclusterConc_an:self_contribution_c) 1.00
## cor(subclusterEM,subclusterConc_an:self_contribution_c) 1.00
## cor(subclusterPS,subclusterConc_an:self_contribution_c) 1.00
## cor(subclusterSS,subclusterConc_an:self_contribution_c) 1.00
## cor(self_contribution_c,subclusterConc_an:self_contribution_c) 1.00
## cor(Intercept,subclusterConc_in:self_contribution_c) 1.00
## cor(subclusterConc_an,subclusterConc_in:self_contribution_c) 1.00
## cor(subclusterConc_in,subclusterConc_in:self_contribution_c) 1.00
## cor(subclusterEM,subclusterConc_in:self_contribution_c) 1.00
## cor(subclusterPS,subclusterConc_in:self_contribution_c) 1.00
## cor(subclusterSS,subclusterConc_in:self_contribution_c) 1.00
## cor(self_contribution_c,subclusterConc_in:self_contribution_c) 1.00
## cor(subclusterConc_an:self_contribution_c,subclusterConc_in:self_contribution_c) 1.00
## cor(Intercept,subclusterEM:self_contribution_c) 1.00
## cor(subclusterConc_an,subclusterEM:self_contribution_c) 1.00
## cor(subclusterConc_in,subclusterEM:self_contribution_c) 1.00
## cor(subclusterEM,subclusterEM:self_contribution_c) 1.00
## cor(subclusterPS,subclusterEM:self_contribution_c) 1.00
## cor(subclusterSS,subclusterEM:self_contribution_c) 1.00
## cor(self_contribution_c,subclusterEM:self_contribution_c) 1.00
## cor(subclusterConc_an:self_contribution_c,subclusterEM:self_contribution_c) 1.00
## cor(subclusterConc_in:self_contribution_c,subclusterEM:self_contribution_c) 1.00
## cor(Intercept,subclusterPS:self_contribution_c) 1.00
## cor(subclusterConc_an,subclusterPS:self_contribution_c) 1.00
## cor(subclusterConc_in,subclusterPS:self_contribution_c) 1.00
## cor(subclusterEM,subclusterPS:self_contribution_c) 1.00
## cor(subclusterPS,subclusterPS:self_contribution_c) 1.00
## cor(subclusterSS,subclusterPS:self_contribution_c) 1.00
## cor(self_contribution_c,subclusterPS:self_contribution_c) 1.00
## cor(subclusterConc_an:self_contribution_c,subclusterPS:self_contribution_c) 1.00
## cor(subclusterConc_in:self_contribution_c,subclusterPS:self_contribution_c) 1.00
## cor(subclusterEM:self_contribution_c,subclusterPS:self_contribution_c) 1.00
## cor(Intercept,subclusterSS:self_contribution_c) 1.00
## cor(subclusterConc_an,subclusterSS:self_contribution_c) 1.00
## cor(subclusterConc_in,subclusterSS:self_contribution_c) 1.00
## cor(subclusterEM,subclusterSS:self_contribution_c) 1.00
## cor(subclusterPS,subclusterSS:self_contribution_c) 1.00
## cor(subclusterSS,subclusterSS:self_contribution_c) 1.00
## cor(self_contribution_c,subclusterSS:self_contribution_c) 1.00
## cor(subclusterConc_an:self_contribution_c,subclusterSS:self_contribution_c) 1.00
## cor(subclusterConc_in:self_contribution_c,subclusterSS:self_contribution_c) 1.00
## cor(subclusterEM:self_contribution_c,subclusterSS:self_contribution_c) 1.00
## cor(subclusterPS:self_contribution_c,subclusterSS:self_contribution_c) 1.00
## Bulk_ESS
## sd(Intercept) 2759
## sd(subclusterConc_an) 2095
## sd(subclusterConc_in) 2172
## sd(subclusterEM) 1945
## sd(subclusterPS) 1357
## sd(subclusterSS) 2636
## sd(self_contribution_c) 1831
## sd(subclusterConc_an:self_contribution_c) 1698
## sd(subclusterConc_in:self_contribution_c) 1707
## sd(subclusterEM:self_contribution_c) 2210
## sd(subclusterPS:self_contribution_c) 2076
## sd(subclusterSS:self_contribution_c) 2131
## cor(Intercept,subclusterConc_an) 5361
## cor(Intercept,subclusterConc_in) 5518
## cor(subclusterConc_an,subclusterConc_in) 3293
## cor(Intercept,subclusterEM) 14840
## cor(subclusterConc_an,subclusterEM) 9193
## cor(subclusterConc_in,subclusterEM) 9183
## cor(Intercept,subclusterPS) 10298
## cor(subclusterConc_an,subclusterPS) 4968
## cor(subclusterConc_in,subclusterPS) 6614
## cor(subclusterEM,subclusterPS) 3689
## cor(Intercept,subclusterSS) 14361
## cor(subclusterConc_an,subclusterSS) 10547
## cor(subclusterConc_in,subclusterSS) 11658
## cor(subclusterEM,subclusterSS) 9059
## cor(subclusterPS,subclusterSS) 9250
## cor(Intercept,self_contribution_c) 5666
## cor(subclusterConc_an,self_contribution_c) 2656
## cor(subclusterConc_in,self_contribution_c) 3467
## cor(subclusterEM,self_contribution_c) 1457
## cor(subclusterPS,self_contribution_c) 1809
## cor(subclusterSS,self_contribution_c) 2088
## cor(Intercept,subclusterConc_an:self_contribution_c) 9655
## cor(subclusterConc_an,subclusterConc_an:self_contribution_c) 8913
## cor(subclusterConc_in,subclusterConc_an:self_contribution_c) 9449
## cor(subclusterEM,subclusterConc_an:self_contribution_c) 4799
## cor(subclusterPS,subclusterConc_an:self_contribution_c) 6049
## cor(subclusterSS,subclusterConc_an:self_contribution_c) 5761
## cor(self_contribution_c,subclusterConc_an:self_contribution_c) 7016
## cor(Intercept,subclusterConc_in:self_contribution_c) 10215
## cor(subclusterConc_an,subclusterConc_in:self_contribution_c) 8531
## cor(subclusterConc_in,subclusterConc_in:self_contribution_c) 10823
## cor(subclusterEM,subclusterConc_in:self_contribution_c) 5675
## cor(subclusterPS,subclusterConc_in:self_contribution_c) 5120
## cor(subclusterSS,subclusterConc_in:self_contribution_c) 7649
## cor(self_contribution_c,subclusterConc_in:self_contribution_c) 7428
## cor(subclusterConc_an:self_contribution_c,subclusterConc_in:self_contribution_c) 3016
## cor(Intercept,subclusterEM:self_contribution_c) 11341
## cor(subclusterConc_an,subclusterEM:self_contribution_c) 9133
## cor(subclusterConc_in,subclusterEM:self_contribution_c) 9144
## cor(subclusterEM,subclusterEM:self_contribution_c) 5367
## cor(subclusterPS,subclusterEM:self_contribution_c) 5031
## cor(subclusterSS,subclusterEM:self_contribution_c) 6484
## cor(self_contribution_c,subclusterEM:self_contribution_c) 5012
## cor(subclusterConc_an:self_contribution_c,subclusterEM:self_contribution_c) 6919
## cor(subclusterConc_in:self_contribution_c,subclusterEM:self_contribution_c) 6273
## cor(Intercept,subclusterPS:self_contribution_c) 12012
## cor(subclusterConc_an,subclusterPS:self_contribution_c) 10507
## cor(subclusterConc_in,subclusterPS:self_contribution_c) 11883
## cor(subclusterEM,subclusterPS:self_contribution_c) 7854
## cor(subclusterPS,subclusterPS:self_contribution_c) 9777
## cor(subclusterSS,subclusterPS:self_contribution_c) 8595
## cor(self_contribution_c,subclusterPS:self_contribution_c) 10564
## cor(subclusterConc_an:self_contribution_c,subclusterPS:self_contribution_c) 8976
## cor(subclusterConc_in:self_contribution_c,subclusterPS:self_contribution_c) 8450
## cor(subclusterEM:self_contribution_c,subclusterPS:self_contribution_c) 8628
## cor(Intercept,subclusterSS:self_contribution_c) 11567
## cor(subclusterConc_an,subclusterSS:self_contribution_c) 9050
## cor(subclusterConc_in,subclusterSS:self_contribution_c) 9150
## cor(subclusterEM,subclusterSS:self_contribution_c) 6721
## cor(subclusterPS,subclusterSS:self_contribution_c) 8301
## cor(subclusterSS,subclusterSS:self_contribution_c) 6826
## cor(self_contribution_c,subclusterSS:self_contribution_c) 7858
## cor(subclusterConc_an:self_contribution_c,subclusterSS:self_contribution_c) 7509
## cor(subclusterConc_in:self_contribution_c,subclusterSS:self_contribution_c) 7379
## cor(subclusterEM:self_contribution_c,subclusterSS:self_contribution_c) 8064
## cor(subclusterPS:self_contribution_c,subclusterSS:self_contribution_c) 7988
## Tail_ESS
## sd(Intercept) 5587
## sd(subclusterConc_an) 3012
## sd(subclusterConc_in) 3793
## sd(subclusterEM) 3478
## sd(subclusterPS) 2489
## sd(subclusterSS) 4349
## sd(self_contribution_c) 2502
## sd(subclusterConc_an:self_contribution_c) 3790
## sd(subclusterConc_in:self_contribution_c) 3358
## sd(subclusterEM:self_contribution_c) 4456
## sd(subclusterPS:self_contribution_c) 4062
## sd(subclusterSS:self_contribution_c) 4128
## cor(Intercept,subclusterConc_an) 6777
## cor(Intercept,subclusterConc_in) 7496
## cor(subclusterConc_an,subclusterConc_in) 5743
## cor(Intercept,subclusterEM) 9087
## cor(subclusterConc_an,subclusterEM) 8656
## cor(subclusterConc_in,subclusterEM) 8642
## cor(Intercept,subclusterPS) 8655
## cor(subclusterConc_an,subclusterPS) 7128
## cor(subclusterConc_in,subclusterPS) 7720
## cor(subclusterEM,subclusterPS) 6998
## cor(Intercept,subclusterSS) 8252
## cor(subclusterConc_an,subclusterSS) 8668
## cor(subclusterConc_in,subclusterSS) 9608
## cor(subclusterEM,subclusterSS) 10055
## cor(subclusterPS,subclusterSS) 8737
## cor(Intercept,self_contribution_c) 8162
## cor(subclusterConc_an,self_contribution_c) 4717
## cor(subclusterConc_in,self_contribution_c) 6288
## cor(subclusterEM,self_contribution_c) 3596
## cor(subclusterPS,self_contribution_c) 3448
## cor(subclusterSS,self_contribution_c) 4276
## cor(Intercept,subclusterConc_an:self_contribution_c) 8264
## cor(subclusterConc_an,subclusterConc_an:self_contribution_c) 8652
## cor(subclusterConc_in,subclusterConc_an:self_contribution_c) 9308
## cor(subclusterEM,subclusterConc_an:self_contribution_c) 8520
## cor(subclusterPS,subclusterConc_an:self_contribution_c) 8897
## cor(subclusterSS,subclusterConc_an:self_contribution_c) 8443
## cor(self_contribution_c,subclusterConc_an:self_contribution_c) 7868
## cor(Intercept,subclusterConc_in:self_contribution_c) 7451
## cor(subclusterConc_an,subclusterConc_in:self_contribution_c) 9204
## cor(subclusterConc_in,subclusterConc_in:self_contribution_c) 8284
## cor(subclusterEM,subclusterConc_in:self_contribution_c) 7924
## cor(subclusterPS,subclusterConc_in:self_contribution_c) 9051
## cor(subclusterSS,subclusterConc_in:self_contribution_c) 9160
## cor(self_contribution_c,subclusterConc_in:self_contribution_c) 9257
## cor(subclusterConc_an:self_contribution_c,subclusterConc_in:self_contribution_c) 6450
## cor(Intercept,subclusterEM:self_contribution_c) 7977
## cor(subclusterConc_an,subclusterEM:self_contribution_c) 8335
## cor(subclusterConc_in,subclusterEM:self_contribution_c) 9217
## cor(subclusterEM,subclusterEM:self_contribution_c) 7501
## cor(subclusterPS,subclusterEM:self_contribution_c) 8041
## cor(subclusterSS,subclusterEM:self_contribution_c) 8845
## cor(self_contribution_c,subclusterEM:self_contribution_c) 8257
## cor(subclusterConc_an:self_contribution_c,subclusterEM:self_contribution_c) 9112
## cor(subclusterConc_in:self_contribution_c,subclusterEM:self_contribution_c) 9469
## cor(Intercept,subclusterPS:self_contribution_c) 8645
## cor(subclusterConc_an,subclusterPS:self_contribution_c) 9035
## cor(subclusterConc_in,subclusterPS:self_contribution_c) 9062
## cor(subclusterEM,subclusterPS:self_contribution_c) 9328
## cor(subclusterPS,subclusterPS:self_contribution_c) 9630
## cor(subclusterSS,subclusterPS:self_contribution_c) 9044
## cor(self_contribution_c,subclusterPS:self_contribution_c) 9875
## cor(subclusterConc_an:self_contribution_c,subclusterPS:self_contribution_c) 9975
## cor(subclusterConc_in:self_contribution_c,subclusterPS:self_contribution_c) 9708
## cor(subclusterEM:self_contribution_c,subclusterPS:self_contribution_c) 10203
## cor(Intercept,subclusterSS:self_contribution_c) 7924
## cor(subclusterConc_an,subclusterSS:self_contribution_c) 7797
## cor(subclusterConc_in,subclusterSS:self_contribution_c) 7576
## cor(subclusterEM,subclusterSS:self_contribution_c) 9121
## cor(subclusterPS,subclusterSS:self_contribution_c) 9340
## cor(subclusterSS,subclusterSS:self_contribution_c) 8861
## cor(self_contribution_c,subclusterSS:self_contribution_c) 8064
## cor(subclusterConc_an:self_contribution_c,subclusterSS:self_contribution_c) 9548
## cor(subclusterConc_in:self_contribution_c,subclusterSS:self_contribution_c) 10200
## cor(subclusterEM:self_contribution_c,subclusterSS:self_contribution_c) 10121
## cor(subclusterPS:self_contribution_c,subclusterSS:self_contribution_c) 9628
##
## ~word (Number of levels: 32)
## Estimate Est.Error l-95% CI u-95% CI Rhat
## sd(Intercept) 0.14 0.10 0.01 0.36 1.00
## sd(self_contribution_c) 0.01 0.01 0.00 0.02 1.00
## cor(Intercept,self_contribution_c) 0.19 0.55 -0.90 0.97 1.00
## Bulk_ESS Tail_ESS
## sd(Intercept) 3960 4438
## sd(self_contribution_c) 3030 4923
## cor(Intercept,self_contribution_c) 4787 7580
##
## Population-Level Effects:
## Estimate Est.Error l-95% CI u-95% CI Rhat
## Intercept[1] -5.96 0.44 -6.84 -5.09 1.00
## Intercept[2] -2.03 0.35 -2.73 -1.35 1.00
## Intercept[3] 0.89 0.35 0.23 1.57 1.00
## Intercept[4] 3.33 0.37 2.59 4.07 1.00
## Intercept[5] 6.16 0.46 5.29 7.09 1.00
## subclusterConc_an -0.13 0.30 -0.72 0.45 1.00
## subclusterConc_in 0.00 0.31 -0.61 0.62 1.00
## subclusterEM 0.12 0.28 -0.43 0.67 1.00
## subclusterPS -0.15 0.31 -0.78 0.44 1.00
## subclusterSS -0.27 0.33 -0.93 0.36 1.00
## self_contribution_c 0.06 0.02 0.04 0.09 1.00
## difficulty_c -0.04 0.00 -0.04 -0.03 1.00
## subclusterConc_an:self_contribution_c -0.02 0.02 -0.05 0.01 1.00
## subclusterConc_in:self_contribution_c -0.00 0.02 -0.04 0.03 1.00
## subclusterEM:self_contribution_c 0.00 0.02 -0.03 0.03 1.00
## subclusterPS:self_contribution_c -0.02 0.02 -0.05 0.02 1.00
## subclusterSS:self_contribution_c -0.01 0.02 -0.05 0.03 1.00
## Bulk_ESS Tail_ESS
## Intercept[1] 2707 5030
## Intercept[2] 2654 4460
## Intercept[3] 2555 4743
## Intercept[4] 2423 4220
## Intercept[5] 2649 5530
## subclusterConc_an 5624 7214
## subclusterConc_in 5581 6793
## subclusterEM 6802 8157
## subclusterPS 6577 7619
## subclusterSS 7124 8546
## self_contribution_c 4271 6278
## difficulty_c 7499 8787
## subclusterConc_an:self_contribution_c 5212 6643
## subclusterConc_in:self_contribution_c 5008 7344
## subclusterEM:self_contribution_c 5883 7399
## subclusterPS:self_contribution_c 6065 7495
## subclusterSS:self_contribution_c 6671 7369
##
## Family Specific Parameters:
## Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
## disc 1.00 0.00 1.00 1.00 NA NA NA
##
## Draws were sampled using sampling(NUTS). For each parameter, Bulk_ESS
## and Tail_ESS are effective sample size measures, and Rhat is the potential
## scale reduction factor on split chains (at convergence, Rhat = 1).Perform hypothesis tests on the fixed effects coefficient:
hypothesis(subcluster_self_mdl,
'self_contribution_c > 0')## Hypothesis Tests for class b:
## Hypothesis Estimate Est.Error CI.Lower CI.Upper Evid.Ratio
## 1 (self_contributio... > 0 0.06 0.02 0.04 0.09 Inf
## Post.Prob Star
## 1 1 *
## ---
## 'CI': 90%-CI for one-sided and 95%-CI for two-sided hypotheses.
## '*': For one-sided hypotheses, the posterior probability exceeds 95%;
## for two-sided hypotheses, the value tested against lies outside the 95%-CI.
## Posterior probabilities of point hypotheses assume equal prior probabilities.hypothesis(subcluster_self_mdl,
'difficulty_c < 0')## Hypothesis Tests for class b:
## Hypothesis Estimate Est.Error CI.Lower CI.Upper Evid.Ratio Post.Prob
## 1 (difficulty_c) < 0 -0.04 0 -0.04 -0.03 Inf 1
## Star
## 1 *
## ---
## 'CI': 90%-CI for one-sided and 95%-CI for two-sided hypotheses.
## '*': For one-sided hypotheses, the posterior probability exceeds 95%;
## for two-sided hypotheses, the value tested against lies outside the 95%-CI.
## Posterior probabilities of point hypotheses assume equal prior probabilities.hypothesis(subcluster_self_mdl,
'subclusterConc_an:self_contribution_c < 0') # PSTQ is reference## Hypothesis Tests for class b:
## Hypothesis Estimate Est.Error CI.Lower CI.Upper Evid.Ratio
## 1 (subclusterConc_a... < 0 -0.02 0.02 -0.05 0.01 7.22
## Post.Prob Star
## 1 0.88
## ---
## 'CI': 90%-CI for one-sided and 95%-CI for two-sided hypotheses.
## '*': For one-sided hypotheses, the posterior probability exceeds 95%;
## for two-sided hypotheses, the value tested against lies outside the 95%-CI.
## Posterior probabilities of point hypotheses assume equal prior probabilities.hypothesis(subcluster_self_mdl,
'subclusterConc_in:self_contribution_c < 0') # PSTQ is reference## Hypothesis Tests for class b:
## Hypothesis Estimate Est.Error CI.Lower CI.Upper Evid.Ratio
## 1 (subclusterConc_i... < 0 0 0.02 -0.03 0.03 1.33
## Post.Prob Star
## 1 0.57
## ---
## 'CI': 90%-CI for one-sided and 95%-CI for two-sided hypotheses.
## '*': For one-sided hypotheses, the posterior probability exceeds 95%;
## for two-sided hypotheses, the value tested against lies outside the 95%-CI.
## Posterior probabilities of point hypotheses assume equal prior probabilities.hypothesis(subcluster_self_mdl,
'subclusterEM:self_contribution_c < 0') # PSTQ is reference## Hypothesis Tests for class b:
## Hypothesis Estimate Est.Error CI.Lower CI.Upper Evid.Ratio
## 1 (subclusterEM:sel... < 0 0 0.02 -0.03 0.03 0.94
## Post.Prob Star
## 1 0.48
## ---
## 'CI': 90%-CI for one-sided and 95%-CI for two-sided hypotheses.
## '*': For one-sided hypotheses, the posterior probability exceeds 95%;
## for two-sided hypotheses, the value tested against lies outside the 95%-CI.
## Posterior probabilities of point hypotheses assume equal prior probabilities.hypothesis(subcluster_self_mdl,
'subclusterPS:self_contribution_c < 0') # PSTQ is reference## Hypothesis Tests for class b:
## Hypothesis Estimate Est.Error CI.Lower CI.Upper Evid.Ratio
## 1 (subclusterPS:sel... < 0 -0.02 0.02 -0.04 0.01 4.18
## Post.Prob Star
## 1 0.81
## ---
## 'CI': 90%-CI for one-sided and 95%-CI for two-sided hypotheses.
## '*': For one-sided hypotheses, the posterior probability exceeds 95%;
## for two-sided hypotheses, the value tested against lies outside the 95%-CI.
## Posterior probabilities of point hypotheses assume equal prior probabilities.hypothesis(subcluster_self_mdl,
'subclusterSS:self_contribution_c < 0') # PSTQ is reference## Hypothesis Tests for class b:
## Hypothesis Estimate Est.Error CI.Lower CI.Upper Evid.Ratio
## 1 (subclusterSS:sel... < 0 -0.01 0.02 -0.04 0.03 1.77
## Post.Prob Star
## 1 0.64
## ---
## 'CI': 90%-CI for one-sided and 95%-CI for two-sided hypotheses.
## '*': For one-sided hypotheses, the posterior probability exceeds 95%;
## for two-sided hypotheses, the value tested against lies outside the 95%-CI.
## Posterior probabilities of point hypotheses assume equal prior probabilities.Re-do the self main model, the one with closeness_01 as
dependent variable, this time also with a difficulty_c
control covariate:
subcluster_dist_self_mdl <- brm(bf(closeness_01 ~
# Fixed effects:
1 +
subcluster +
self_contribution_c +
difficulty_c +
subcluster:self_contribution_c +
# Random effects:
(1 +
subcluster +
self_contribution_c +
subcluster:self_contribution_c|participant) +
(1 + self_contribution_c|word),
phi ~ 1 + subcluster),
data = df,
family = Beta,
# MCMC settings:
seed = 42,
init = 0,
cores = 4,
iter = 6000,
warmup = 3000,
control = list(adapt_delta = 0.99))
# Save model:
save(subcluster_dist_self_mdl,
file = '../models_E2/subcluster_dist_self_mdl.RData')Load model:
load('../models_E2/subcluster_dist_self_mdl.Rdata')Show priors:
prior_summary(subcluster_dist_self_mdl)## prior class coef
## (flat) b
## (flat) b difficulty_c
## (flat) b self_contribution_c
## (flat) b subclusterConc_an
## (flat) b subclusterConc_an:self_contribution_c
## (flat) b subclusterConc_in
## (flat) b subclusterConc_in:self_contribution_c
## (flat) b subclusterEM
## (flat) b subclusterEM:self_contribution_c
## (flat) b subclusterPS
## (flat) b subclusterPS:self_contribution_c
## (flat) b subclusterSS
## (flat) b subclusterSS:self_contribution_c
## (flat) b
## (flat) b subclusterConc_an
## (flat) b subclusterConc_in
## (flat) b subclusterEM
## (flat) b subclusterPS
## (flat) b subclusterSS
## student_t(3, 0, 2.5) Intercept
## student_t(3, 0, 2.5) Intercept
## lkj_corr_cholesky(1) L
## lkj_corr_cholesky(1) L
## lkj_corr_cholesky(1) L
## student_t(3, 0, 2.5) sd
## student_t(3, 0, 2.5) sd
## student_t(3, 0, 2.5) sd Intercept
## student_t(3, 0, 2.5) sd self_contribution_c
## student_t(3, 0, 2.5) sd subclusterConc_an
## student_t(3, 0, 2.5) sd subclusterConc_an:self_contribution_c
## student_t(3, 0, 2.5) sd subclusterConc_in
## student_t(3, 0, 2.5) sd subclusterConc_in:self_contribution_c
## student_t(3, 0, 2.5) sd subclusterEM
## student_t(3, 0, 2.5) sd subclusterEM:self_contribution_c
## student_t(3, 0, 2.5) sd subclusterPS
## student_t(3, 0, 2.5) sd subclusterPS:self_contribution_c
## student_t(3, 0, 2.5) sd subclusterSS
## student_t(3, 0, 2.5) sd subclusterSS:self_contribution_c
## student_t(3, 0, 2.5) sd
## student_t(3, 0, 2.5) sd Intercept
## student_t(3, 0, 2.5) sd self_contribution_c
## group resp dpar nlpar lb ub source
## default
## (vectorized)
## (vectorized)
## (vectorized)
## (vectorized)
## (vectorized)
## (vectorized)
## (vectorized)
## (vectorized)
## (vectorized)
## (vectorized)
## (vectorized)
## (vectorized)
## phi default
## phi (vectorized)
## phi (vectorized)
## phi (vectorized)
## phi (vectorized)
## phi (vectorized)
## default
## phi default
## default
## participant (vectorized)
## word (vectorized)
## 0 default
## participant 0 (vectorized)
## participant 0 (vectorized)
## participant 0 (vectorized)
## participant 0 (vectorized)
## participant 0 (vectorized)
## participant 0 (vectorized)
## participant 0 (vectorized)
## participant 0 (vectorized)
## participant 0 (vectorized)
## participant 0 (vectorized)
## participant 0 (vectorized)
## participant 0 (vectorized)
## participant 0 (vectorized)
## word 0 (vectorized)
## word 0 (vectorized)
## word 0 (vectorized)Check posterior predictive checks of the mixed beta regression:
pp_check(subcluster_dist_self_mdl, ndraws = 100)
Check this model:
subcluster_dist_self_mdl## Warning: Parts of the model have not converged (some Rhats are > 1.05). Be
## careful when analysing the results! We recommend running more iterations and/or
## setting stronger priors.## Warning: There were 252 divergent transitions after warmup. Increasing
## adapt_delta above 0.99 may help. See
## http://mc-stan.org/misc/warnings.html#divergent-transitions-after-warmup## Family: beta
## Links: mu = logit; phi = log
## Formula: closeness_01 ~ 1 + subcluster + self_contribution_c + difficulty_c + subcluster:self_contribution_c + (1 + subcluster + self_contribution_c + subcluster:self_contribution_c | participant) + (1 + self_contribution_c | word)
## phi ~ 1 + subcluster
## Data: df (Number of observations: 1032)
## Draws: 4 chains, each with iter = 6000; warmup = 3000; thin = 1;
## total post-warmup draws = 12000
##
## Group-Level Effects:
## ~participant (Number of levels: 129)
## Estimate
## sd(Intercept) 0.84
## sd(subclusterConc_an) 0.62
## sd(subclusterConc_in) 0.49
## sd(subclusterEM) 0.37
## sd(subclusterPS) 0.61
## sd(subclusterSS) 0.32
## sd(self_contribution_c) 0.02
## sd(subclusterConc_an:self_contribution_c) 0.01
## sd(subclusterConc_in:self_contribution_c) 0.00
## sd(subclusterEM:self_contribution_c) 0.01
## sd(subclusterPS:self_contribution_c) 0.02
## sd(subclusterSS:self_contribution_c) 0.01
## cor(Intercept,subclusterConc_an) -0.19
## cor(Intercept,subclusterConc_in) -0.16
## cor(subclusterConc_an,subclusterConc_in) 0.88
## cor(Intercept,subclusterEM) -0.03
## cor(subclusterConc_an,subclusterEM) 0.18
## cor(subclusterConc_in,subclusterEM) 0.12
## cor(Intercept,subclusterPS) 0.05
## cor(subclusterConc_an,subclusterPS) 0.08
## cor(subclusterConc_in,subclusterPS) 0.03
## cor(subclusterEM,subclusterPS) 0.27
## cor(Intercept,subclusterSS) 0.19
## cor(subclusterConc_an,subclusterSS) -0.02
## cor(subclusterConc_in,subclusterSS) -0.12
## cor(subclusterEM,subclusterSS) 0.10
## cor(subclusterPS,subclusterSS) 0.38
## cor(Intercept,self_contribution_c) 0.04
## cor(subclusterConc_an,self_contribution_c) 0.08
## cor(subclusterConc_in,self_contribution_c) 0.11
## cor(subclusterEM,self_contribution_c) 0.07
## cor(subclusterPS,self_contribution_c) 0.03
## cor(subclusterSS,self_contribution_c) 0.24
## cor(Intercept,subclusterConc_an:self_contribution_c) 0.14
## cor(subclusterConc_an,subclusterConc_an:self_contribution_c) -0.06
## cor(subclusterConc_in,subclusterConc_an:self_contribution_c) -0.04
## cor(subclusterEM,subclusterConc_an:self_contribution_c) -0.01
## cor(subclusterPS,subclusterConc_an:self_contribution_c) -0.12
## cor(subclusterSS,subclusterConc_an:self_contribution_c) -0.03
## cor(self_contribution_c,subclusterConc_an:self_contribution_c) 0.03
## cor(Intercept,subclusterConc_in:self_contribution_c) -0.05
## cor(subclusterConc_an,subclusterConc_in:self_contribution_c) 0.12
## cor(subclusterConc_in,subclusterConc_in:self_contribution_c) 0.12
## cor(subclusterEM,subclusterConc_in:self_contribution_c) -0.15
## cor(subclusterPS,subclusterConc_in:self_contribution_c) -0.07
## cor(subclusterSS,subclusterConc_in:self_contribution_c) 0.04
## cor(self_contribution_c,subclusterConc_in:self_contribution_c) 0.08
## cor(subclusterConc_an:self_contribution_c,subclusterConc_in:self_contribution_c) 0.19
## cor(Intercept,subclusterEM:self_contribution_c) 0.11
## cor(subclusterConc_an,subclusterEM:self_contribution_c) 0.17
## cor(subclusterConc_in,subclusterEM:self_contribution_c) 0.16
## cor(subclusterEM,subclusterEM:self_contribution_c) 0.38
## cor(subclusterPS,subclusterEM:self_contribution_c) 0.01
## cor(subclusterSS,subclusterEM:self_contribution_c) 0.04
## cor(self_contribution_c,subclusterEM:self_contribution_c) 0.21
## cor(subclusterConc_an:self_contribution_c,subclusterEM:self_contribution_c) 0.03
## cor(subclusterConc_in:self_contribution_c,subclusterEM:self_contribution_c) 0.06
## cor(Intercept,subclusterPS:self_contribution_c) 0.24
## cor(subclusterConc_an,subclusterPS:self_contribution_c) -0.19
## cor(subclusterConc_in,subclusterPS:self_contribution_c) -0.33
## cor(subclusterEM,subclusterPS:self_contribution_c) 0.01
## cor(subclusterPS,subclusterPS:self_contribution_c) 0.53
## cor(subclusterSS,subclusterPS:self_contribution_c) 0.44
## cor(self_contribution_c,subclusterPS:self_contribution_c) -0.16
## cor(subclusterConc_an:self_contribution_c,subclusterPS:self_contribution_c) -0.06
## cor(subclusterConc_in:self_contribution_c,subclusterPS:self_contribution_c) -0.12
## cor(subclusterEM:self_contribution_c,subclusterPS:self_contribution_c) -0.06
## cor(Intercept,subclusterSS:self_contribution_c) -0.15
## cor(subclusterConc_an,subclusterSS:self_contribution_c) 0.31
## cor(subclusterConc_in,subclusterSS:self_contribution_c) 0.30
## cor(subclusterEM,subclusterSS:self_contribution_c) 0.06
## cor(subclusterPS,subclusterSS:self_contribution_c) 0.25
## cor(subclusterSS,subclusterSS:self_contribution_c) 0.21
## cor(self_contribution_c,subclusterSS:self_contribution_c) 0.20
## cor(subclusterConc_an:self_contribution_c,subclusterSS:self_contribution_c) -0.04
## cor(subclusterConc_in:self_contribution_c,subclusterSS:self_contribution_c) 0.08
## cor(subclusterEM:self_contribution_c,subclusterSS:self_contribution_c) 0.10
## cor(subclusterPS:self_contribution_c,subclusterSS:self_contribution_c) 0.11
## Est.Error
## sd(Intercept) 0.10
## sd(subclusterConc_an) 0.08
## sd(subclusterConc_in) 0.06
## sd(subclusterEM) 0.06
## sd(subclusterPS) 0.09
## sd(subclusterSS) 0.07
## sd(self_contribution_c) 0.00
## sd(subclusterConc_an:self_contribution_c) 0.00
## sd(subclusterConc_in:self_contribution_c) 0.00
## sd(subclusterEM:self_contribution_c) 0.00
## sd(subclusterPS:self_contribution_c) 0.01
## sd(subclusterSS:self_contribution_c) 0.00
## cor(Intercept,subclusterConc_an) 0.14
## cor(Intercept,subclusterConc_in) 0.13
## cor(subclusterConc_an,subclusterConc_in) 0.04
## cor(Intercept,subclusterEM) 0.14
## cor(subclusterConc_an,subclusterEM) 0.15
## cor(subclusterConc_in,subclusterEM) 0.16
## cor(Intercept,subclusterPS) 0.11
## cor(subclusterConc_an,subclusterPS) 0.14
## cor(subclusterConc_in,subclusterPS) 0.20
## cor(subclusterEM,subclusterPS) 0.23
## cor(Intercept,subclusterSS) 0.16
## cor(subclusterConc_an,subclusterSS) 0.26
## cor(subclusterConc_in,subclusterSS) 0.25
## cor(subclusterEM,subclusterSS) 0.22
## cor(subclusterPS,subclusterSS) 0.25
## cor(Intercept,self_contribution_c) 0.11
## cor(subclusterConc_an,self_contribution_c) 0.16
## cor(subclusterConc_in,self_contribution_c) 0.16
## cor(subclusterEM,self_contribution_c) 0.16
## cor(subclusterPS,self_contribution_c) 0.13
## cor(subclusterSS,self_contribution_c) 0.24
## cor(Intercept,subclusterConc_an:self_contribution_c) 0.24
## cor(subclusterConc_an,subclusterConc_an:self_contribution_c) 0.21
## cor(subclusterConc_in,subclusterConc_an:self_contribution_c) 0.23
## cor(subclusterEM,subclusterConc_an:self_contribution_c) 0.22
## cor(subclusterPS,subclusterConc_an:self_contribution_c) 0.24
## cor(subclusterSS,subclusterConc_an:self_contribution_c) 0.25
## cor(self_contribution_c,subclusterConc_an:self_contribution_c) 0.25
## cor(Intercept,subclusterConc_in:self_contribution_c) 0.22
## cor(subclusterConc_an,subclusterConc_in:self_contribution_c) 0.25
## cor(subclusterConc_in,subclusterConc_in:self_contribution_c) 0.23
## cor(subclusterEM,subclusterConc_in:self_contribution_c) 0.26
## cor(subclusterPS,subclusterConc_in:self_contribution_c) 0.25
## cor(subclusterSS,subclusterConc_in:self_contribution_c) 0.24
## cor(self_contribution_c,subclusterConc_in:self_contribution_c) 0.25
## cor(subclusterConc_an:self_contribution_c,subclusterConc_in:self_contribution_c) 0.28
## cor(Intercept,subclusterEM:self_contribution_c) 0.21
## cor(subclusterConc_an,subclusterEM:self_contribution_c) 0.27
## cor(subclusterConc_in,subclusterEM:self_contribution_c) 0.29
## cor(subclusterEM,subclusterEM:self_contribution_c) 0.21
## cor(subclusterPS,subclusterEM:self_contribution_c) 0.24
## cor(subclusterSS,subclusterEM:self_contribution_c) 0.26
## cor(self_contribution_c,subclusterEM:self_contribution_c) 0.32
## cor(subclusterConc_an:self_contribution_c,subclusterEM:self_contribution_c) 0.23
## cor(subclusterConc_in:self_contribution_c,subclusterEM:self_contribution_c) 0.28
## cor(Intercept,subclusterPS:self_contribution_c) 0.14
## cor(subclusterConc_an,subclusterPS:self_contribution_c) 0.15
## cor(subclusterConc_in,subclusterPS:self_contribution_c) 0.15
## cor(subclusterEM,subclusterPS:self_contribution_c) 0.21
## cor(subclusterPS,subclusterPS:self_contribution_c) 0.15
## cor(subclusterSS,subclusterPS:self_contribution_c) 0.25
## cor(self_contribution_c,subclusterPS:self_contribution_c) 0.17
## cor(subclusterConc_an:self_contribution_c,subclusterPS:self_contribution_c) 0.26
## cor(subclusterConc_in:self_contribution_c,subclusterPS:self_contribution_c) 0.23
## cor(subclusterEM:self_contribution_c,subclusterPS:self_contribution_c) 0.24
## cor(Intercept,subclusterSS:self_contribution_c) 0.22
## cor(subclusterConc_an,subclusterSS:self_contribution_c) 0.18
## cor(subclusterConc_in,subclusterSS:self_contribution_c) 0.18
## cor(subclusterEM,subclusterSS:self_contribution_c) 0.23
## cor(subclusterPS,subclusterSS:self_contribution_c) 0.22
## cor(subclusterSS,subclusterSS:self_contribution_c) 0.25
## cor(self_contribution_c,subclusterSS:self_contribution_c) 0.19
## cor(subclusterConc_an:self_contribution_c,subclusterSS:self_contribution_c) 0.23
## cor(subclusterConc_in:self_contribution_c,subclusterSS:self_contribution_c) 0.33
## cor(subclusterEM:self_contribution_c,subclusterSS:self_contribution_c) 0.24
## cor(subclusterPS:self_contribution_c,subclusterSS:self_contribution_c) 0.23
## l-95% CI
## sd(Intercept) 0.67
## sd(subclusterConc_an) 0.48
## sd(subclusterConc_in) 0.37
## sd(subclusterEM) 0.25
## sd(subclusterPS) 0.43
## sd(subclusterSS) 0.12
## sd(self_contribution_c) 0.01
## sd(subclusterConc_an:self_contribution_c) 0.00
## sd(subclusterConc_in:self_contribution_c) 0.00
## sd(subclusterEM:self_contribution_c) 0.00
## sd(subclusterPS:self_contribution_c) 0.01
## sd(subclusterSS:self_contribution_c) 0.00
## cor(Intercept,subclusterConc_an) -0.38
## cor(Intercept,subclusterConc_in) -0.36
## cor(subclusterConc_an,subclusterConc_in) 0.78
## cor(Intercept,subclusterEM) -0.27
## cor(subclusterConc_an,subclusterEM) -0.17
## cor(subclusterConc_in,subclusterEM) -0.22
## cor(Intercept,subclusterPS) -0.17
## cor(subclusterConc_an,subclusterPS) -0.20
## cor(subclusterConc_in,subclusterPS) -0.30
## cor(subclusterEM,subclusterPS) -0.20
## cor(Intercept,subclusterSS) -0.09
## cor(subclusterConc_an,subclusterSS) -0.46
## cor(subclusterConc_in,subclusterSS) -0.53
## cor(subclusterEM,subclusterSS) -0.39
## cor(subclusterPS,subclusterSS) -0.16
## cor(Intercept,self_contribution_c) -0.18
## cor(subclusterConc_an,self_contribution_c) -0.28
## cor(subclusterConc_in,self_contribution_c) -0.25
## cor(subclusterEM,self_contribution_c) -0.29
## cor(subclusterPS,self_contribution_c) -0.26
## cor(subclusterSS,self_contribution_c) -0.16
## cor(Intercept,subclusterConc_an:self_contribution_c) -0.42
## cor(subclusterConc_an,subclusterConc_an:self_contribution_c) -0.49
## cor(subclusterConc_in,subclusterConc_an:self_contribution_c) -0.55
## cor(subclusterEM,subclusterConc_an:self_contribution_c) -0.44
## cor(subclusterPS,subclusterConc_an:self_contribution_c) -0.56
## cor(subclusterSS,subclusterConc_an:self_contribution_c) -0.56
## cor(self_contribution_c,subclusterConc_an:self_contribution_c) -0.51
## cor(Intercept,subclusterConc_in:self_contribution_c) -0.51
## cor(subclusterConc_an,subclusterConc_in:self_contribution_c) -0.40
## cor(subclusterConc_in,subclusterConc_in:self_contribution_c) -0.40
## cor(subclusterEM,subclusterConc_in:self_contribution_c) -0.71
## cor(subclusterPS,subclusterConc_in:self_contribution_c) -0.60
## cor(subclusterSS,subclusterConc_in:self_contribution_c) -0.46
## cor(self_contribution_c,subclusterConc_in:self_contribution_c) -0.42
## cor(subclusterConc_an:self_contribution_c,subclusterConc_in:self_contribution_c) -0.41
## cor(Intercept,subclusterEM:self_contribution_c) -0.34
## cor(subclusterConc_an,subclusterEM:self_contribution_c) -0.36
## cor(subclusterConc_in,subclusterEM:self_contribution_c) -0.39
## cor(subclusterEM,subclusterEM:self_contribution_c) -0.13
## cor(subclusterPS,subclusterEM:self_contribution_c) -0.47
## cor(subclusterSS,subclusterEM:self_contribution_c) -0.49
## cor(self_contribution_c,subclusterEM:self_contribution_c) -0.39
## cor(subclusterConc_an:self_contribution_c,subclusterEM:self_contribution_c) -0.43
## cor(subclusterConc_in:self_contribution_c,subclusterEM:self_contribution_c) -0.48
## cor(Intercept,subclusterPS:self_contribution_c) -0.09
## cor(subclusterConc_an,subclusterPS:self_contribution_c) -0.47
## cor(subclusterConc_in,subclusterPS:self_contribution_c) -0.58
## cor(subclusterEM,subclusterPS:self_contribution_c) -0.42
## cor(subclusterPS,subclusterPS:self_contribution_c) 0.17
## cor(subclusterSS,subclusterPS:self_contribution_c) -0.15
## cor(self_contribution_c,subclusterPS:self_contribution_c) -0.51
## cor(subclusterConc_an:self_contribution_c,subclusterPS:self_contribution_c) -0.53
## cor(subclusterConc_in:self_contribution_c,subclusterPS:self_contribution_c) -0.57
## cor(subclusterEM:self_contribution_c,subclusterPS:self_contribution_c) -0.47
## cor(Intercept,subclusterSS:self_contribution_c) -0.45
## cor(subclusterConc_an,subclusterSS:self_contribution_c) -0.10
## cor(subclusterConc_in,subclusterSS:self_contribution_c) -0.11
## cor(subclusterEM,subclusterSS:self_contribution_c) -0.41
## cor(subclusterPS,subclusterSS:self_contribution_c) -0.27
## cor(subclusterSS,subclusterSS:self_contribution_c) -0.34
## cor(self_contribution_c,subclusterSS:self_contribution_c) -0.24
## cor(subclusterConc_an:self_contribution_c,subclusterSS:self_contribution_c) -0.49
## cor(subclusterConc_in:self_contribution_c,subclusterSS:self_contribution_c) -0.52
## cor(subclusterEM:self_contribution_c,subclusterSS:self_contribution_c) -0.40
## cor(subclusterPS:self_contribution_c,subclusterSS:self_contribution_c) -0.38
## u-95% CI
## sd(Intercept) 0.98
## sd(subclusterConc_an) 0.73
## sd(subclusterConc_in) 0.60
## sd(subclusterEM) 0.52
## sd(subclusterPS) 0.80
## sd(subclusterSS) 0.44
## sd(self_contribution_c) 0.02
## sd(subclusterConc_an:self_contribution_c) 0.02
## sd(subclusterConc_in:self_contribution_c) 0.01
## sd(subclusterEM:self_contribution_c) 0.02
## sd(subclusterPS:self_contribution_c) 0.04
## sd(subclusterSS:self_contribution_c) 0.02
## cor(Intercept,subclusterConc_an) 0.08
## cor(Intercept,subclusterConc_in) 0.10
## cor(subclusterConc_an,subclusterConc_in) 0.95
## cor(Intercept,subclusterEM) 0.29
## cor(subclusterConc_an,subclusterEM) 0.41
## cor(subclusterConc_in,subclusterEM) 0.39
## cor(Intercept,subclusterPS) 0.31
## cor(subclusterConc_an,subclusterPS) 0.32
## cor(subclusterConc_in,subclusterPS) 0.30
## cor(subclusterEM,subclusterPS) 0.59
## cor(Intercept,subclusterSS) 0.55
## cor(subclusterConc_an,subclusterSS) 0.33
## cor(subclusterConc_in,subclusterSS) 0.22
## cor(subclusterEM,subclusterSS) 0.40
## cor(subclusterPS,subclusterSS) 0.67
## cor(Intercept,self_contribution_c) 0.29
## cor(subclusterConc_an,self_contribution_c) 0.36
## cor(subclusterConc_in,self_contribution_c) 0.39
## cor(subclusterEM,self_contribution_c) 0.40
## cor(subclusterPS,self_contribution_c) 0.31
## cor(subclusterSS,self_contribution_c) 0.58
## cor(Intercept,subclusterConc_an:self_contribution_c) 0.48
## cor(subclusterConc_an,subclusterConc_an:self_contribution_c) 0.35
## cor(subclusterConc_in,subclusterConc_an:self_contribution_c) 0.42
## cor(subclusterEM,subclusterConc_an:self_contribution_c) 0.44
## cor(subclusterPS,subclusterConc_an:self_contribution_c) 0.45
## cor(subclusterSS,subclusterConc_an:self_contribution_c) 0.47
## cor(self_contribution_c,subclusterConc_an:self_contribution_c) 0.44
## cor(Intercept,subclusterConc_in:self_contribution_c) 0.36
## cor(subclusterConc_an,subclusterConc_in:self_contribution_c) 0.46
## cor(subclusterConc_in,subclusterConc_in:self_contribution_c) 0.50
## cor(subclusterEM,subclusterConc_in:self_contribution_c) 0.37
## cor(subclusterPS,subclusterConc_in:self_contribution_c) 0.37
## cor(subclusterSS,subclusterConc_in:self_contribution_c) 0.43
## cor(self_contribution_c,subclusterConc_in:self_contribution_c) 0.46
## cor(subclusterConc_an:self_contribution_c,subclusterConc_in:self_contribution_c) 0.64
## cor(Intercept,subclusterEM:self_contribution_c) 0.52
## cor(subclusterConc_an,subclusterEM:self_contribution_c) 0.54
## cor(subclusterConc_in,subclusterEM:self_contribution_c) 0.58
## cor(subclusterEM,subclusterEM:self_contribution_c) 0.74
## cor(subclusterPS,subclusterEM:self_contribution_c) 0.39
## cor(subclusterSS,subclusterEM:self_contribution_c) 0.46
## cor(self_contribution_c,subclusterEM:self_contribution_c) 0.64
## cor(subclusterConc_an:self_contribution_c,subclusterEM:self_contribution_c) 0.53
## cor(subclusterConc_in:self_contribution_c,subclusterEM:self_contribution_c) 0.45
## cor(Intercept,subclusterPS:self_contribution_c) 0.51
## cor(subclusterConc_an,subclusterPS:self_contribution_c) 0.13
## cor(subclusterConc_in,subclusterPS:self_contribution_c) 0.03
## cor(subclusterEM,subclusterPS:self_contribution_c) 0.39
## cor(subclusterPS,subclusterPS:self_contribution_c) 0.77
## cor(subclusterSS,subclusterPS:self_contribution_c) 0.82
## cor(self_contribution_c,subclusterPS:self_contribution_c) 0.21
## cor(subclusterConc_an:self_contribution_c,subclusterPS:self_contribution_c) 0.52
## cor(subclusterConc_in:self_contribution_c,subclusterPS:self_contribution_c) 0.35
## cor(subclusterEM:self_contribution_c,subclusterPS:self_contribution_c) 0.43
## cor(Intercept,subclusterSS:self_contribution_c) 0.31
## cor(subclusterConc_an,subclusterSS:self_contribution_c) 0.62
## cor(subclusterConc_in,subclusterSS:self_contribution_c) 0.62
## cor(subclusterEM,subclusterSS:self_contribution_c) 0.38
## cor(subclusterPS,subclusterSS:self_contribution_c) 0.57
## cor(subclusterSS,subclusterSS:self_contribution_c) 0.53
## cor(self_contribution_c,subclusterSS:self_contribution_c) 0.54
## cor(subclusterConc_an:self_contribution_c,subclusterSS:self_contribution_c) 0.43
## cor(subclusterConc_in:self_contribution_c,subclusterSS:self_contribution_c) 0.51
## cor(subclusterEM:self_contribution_c,subclusterSS:self_contribution_c) 0.53
## cor(subclusterPS:self_contribution_c,subclusterSS:self_contribution_c) 0.56
## Rhat
## sd(Intercept) 1.76
## sd(subclusterConc_an) 1.32
## sd(subclusterConc_in) 1.23
## sd(subclusterEM) 1.26
## sd(subclusterPS) 1.24
## sd(subclusterSS) 1.46
## sd(self_contribution_c) 1.21
## sd(subclusterConc_an:self_contribution_c) 1.18
## sd(subclusterConc_in:self_contribution_c) 1.34
## sd(subclusterEM:self_contribution_c) 1.42
## sd(subclusterPS:self_contribution_c) 1.57
## sd(subclusterSS:self_contribution_c) 1.37
## cor(Intercept,subclusterConc_an) 1.43
## cor(Intercept,subclusterConc_in) 1.20
## cor(subclusterConc_an,subclusterConc_in) 1.26
## cor(Intercept,subclusterEM) 1.13
## cor(subclusterConc_an,subclusterEM) 1.17
## cor(subclusterConc_in,subclusterEM) 1.15
## cor(Intercept,subclusterPS) 1.18
## cor(subclusterConc_an,subclusterPS) 1.27
## cor(subclusterConc_in,subclusterPS) 1.56
## cor(subclusterEM,subclusterPS) 1.64
## cor(Intercept,subclusterSS) 1.22
## cor(subclusterConc_an,subclusterSS) 1.58
## cor(subclusterConc_in,subclusterSS) 1.53
## cor(subclusterEM,subclusterSS) 1.32
## cor(subclusterPS,subclusterSS) 1.63
## cor(Intercept,self_contribution_c) 1.26
## cor(subclusterConc_an,self_contribution_c) 1.49
## cor(subclusterConc_in,self_contribution_c) 1.44
## cor(subclusterEM,self_contribution_c) 1.26
## cor(subclusterPS,self_contribution_c) 1.31
## cor(subclusterSS,self_contribution_c) 1.43
## cor(Intercept,subclusterConc_an:self_contribution_c) 1.21
## cor(subclusterConc_an,subclusterConc_an:self_contribution_c) 1.28
## cor(subclusterConc_in,subclusterConc_an:self_contribution_c) 1.39
## cor(subclusterEM,subclusterConc_an:self_contribution_c) 1.38
## cor(subclusterPS,subclusterConc_an:self_contribution_c) 1.36
## cor(subclusterSS,subclusterConc_an:self_contribution_c) 1.22
## cor(self_contribution_c,subclusterConc_an:self_contribution_c) 1.29
## cor(Intercept,subclusterConc_in:self_contribution_c) 1.23
## cor(subclusterConc_an,subclusterConc_in:self_contribution_c) 1.21
## cor(subclusterConc_in,subclusterConc_in:self_contribution_c) 1.10
## cor(subclusterEM,subclusterConc_in:self_contribution_c) 1.49
## cor(subclusterPS,subclusterConc_in:self_contribution_c) 1.19
## cor(subclusterSS,subclusterConc_in:self_contribution_c) 1.20
## cor(self_contribution_c,subclusterConc_in:self_contribution_c) 1.28
## cor(subclusterConc_an:self_contribution_c,subclusterConc_in:self_contribution_c) 1.14
## cor(Intercept,subclusterEM:self_contribution_c) 1.18
## cor(subclusterConc_an,subclusterEM:self_contribution_c) 1.41
## cor(subclusterConc_in,subclusterEM:self_contribution_c) 1.49
## cor(subclusterEM,subclusterEM:self_contribution_c) 1.28
## cor(subclusterPS,subclusterEM:self_contribution_c) 1.24
## cor(subclusterSS,subclusterEM:self_contribution_c) 1.20
## cor(self_contribution_c,subclusterEM:self_contribution_c) 1.41
## cor(subclusterConc_an:self_contribution_c,subclusterEM:self_contribution_c) 1.25
## cor(subclusterConc_in:self_contribution_c,subclusterEM:self_contribution_c) 1.29
## cor(Intercept,subclusterPS:self_contribution_c) 1.19
## cor(subclusterConc_an,subclusterPS:self_contribution_c) 1.13
## cor(subclusterConc_in,subclusterPS:self_contribution_c) 1.11
## cor(subclusterEM,subclusterPS:self_contribution_c) 1.29
## cor(subclusterPS,subclusterPS:self_contribution_c) 1.19
## cor(subclusterSS,subclusterPS:self_contribution_c) 1.60
## cor(self_contribution_c,subclusterPS:self_contribution_c) 1.27
## cor(subclusterConc_an:self_contribution_c,subclusterPS:self_contribution_c) 1.42
## cor(subclusterConc_in:self_contribution_c,subclusterPS:self_contribution_c) 1.25
## cor(subclusterEM:self_contribution_c,subclusterPS:self_contribution_c) 1.20
## cor(Intercept,subclusterSS:self_contribution_c) 1.31
## cor(subclusterConc_an,subclusterSS:self_contribution_c) 1.11
## cor(subclusterConc_in,subclusterSS:self_contribution_c) 1.11
## cor(subclusterEM,subclusterSS:self_contribution_c) 1.18
## cor(subclusterPS,subclusterSS:self_contribution_c) 1.20
## cor(subclusterSS,subclusterSS:self_contribution_c) 1.33
## cor(self_contribution_c,subclusterSS:self_contribution_c) 1.22
## cor(subclusterConc_an:self_contribution_c,subclusterSS:self_contribution_c) 1.26
## cor(subclusterConc_in:self_contribution_c,subclusterSS:self_contribution_c) 1.52
## cor(subclusterEM:self_contribution_c,subclusterSS:self_contribution_c) 1.15
## cor(subclusterPS:self_contribution_c,subclusterSS:self_contribution_c) 1.18
## Bulk_ESS
## sd(Intercept) 6
## sd(subclusterConc_an) 10
## sd(subclusterConc_in) 13
## sd(subclusterEM) 38
## sd(subclusterPS) 14
## sd(subclusterSS) 81
## sd(self_contribution_c) 14
## sd(subclusterConc_an:self_contribution_c) 70
## sd(subclusterConc_in:self_contribution_c) 48
## sd(subclusterEM:self_contribution_c) 8
## sd(subclusterPS:self_contribution_c) 11
## sd(subclusterSS:self_contribution_c) 20
## cor(Intercept,subclusterConc_an) 8
## cor(Intercept,subclusterConc_in) 15
## cor(subclusterConc_an,subclusterConc_in) 20
## cor(Intercept,subclusterEM) 24
## cor(subclusterConc_an,subclusterEM) 18
## cor(subclusterConc_in,subclusterEM) 22
## cor(Intercept,subclusterPS) 39
## cor(subclusterConc_an,subclusterPS) 12
## cor(subclusterConc_in,subclusterPS) 7
## cor(subclusterEM,subclusterPS) 7
## cor(Intercept,subclusterSS) 35
## cor(subclusterConc_an,subclusterSS) 7
## cor(subclusterConc_in,subclusterSS) 7
## cor(subclusterEM,subclusterSS) 10
## cor(subclusterPS,subclusterSS) 7
## cor(Intercept,self_contribution_c) 78
## cor(subclusterConc_an,self_contribution_c) 10
## cor(subclusterConc_in,self_contribution_c) 12
## cor(subclusterEM,self_contribution_c) 28
## cor(subclusterPS,self_contribution_c) 37
## cor(subclusterSS,self_contribution_c) 9
## cor(Intercept,subclusterConc_an:self_contribution_c) 15
## cor(subclusterConc_an,subclusterConc_an:self_contribution_c) 22
## cor(subclusterConc_in,subclusterConc_an:self_contribution_c) 28
## cor(subclusterEM,subclusterConc_an:self_contribution_c) 64
## cor(subclusterPS,subclusterConc_an:self_contribution_c) 74
## cor(subclusterSS,subclusterConc_an:self_contribution_c) 66
## cor(self_contribution_c,subclusterConc_an:self_contribution_c) 11
## cor(Intercept,subclusterConc_in:self_contribution_c) 62
## cor(subclusterConc_an,subclusterConc_in:self_contribution_c) 13
## cor(subclusterConc_in,subclusterConc_in:self_contribution_c) 28
## cor(subclusterEM,subclusterConc_in:self_contribution_c) 28
## cor(subclusterPS,subclusterConc_in:self_contribution_c) 16
## cor(subclusterSS,subclusterConc_in:self_contribution_c) 14
## cor(self_contribution_c,subclusterConc_in:self_contribution_c) 11
## cor(subclusterConc_an:self_contribution_c,subclusterConc_in:self_contribution_c) 19
## cor(Intercept,subclusterEM:self_contribution_c) 18
## cor(subclusterConc_an,subclusterEM:self_contribution_c) 8
## cor(subclusterConc_in,subclusterEM:self_contribution_c) 8
## cor(subclusterEM,subclusterEM:self_contribution_c) 94
## cor(subclusterPS,subclusterEM:self_contribution_c) 12
## cor(subclusterSS,subclusterEM:self_contribution_c) 15
## cor(self_contribution_c,subclusterEM:self_contribution_c) 9
## cor(subclusterConc_an:self_contribution_c,subclusterEM:self_contribution_c) 108
## cor(subclusterConc_in:self_contribution_c,subclusterEM:self_contribution_c) 11
## cor(Intercept,subclusterPS:self_contribution_c) 24
## cor(subclusterConc_an,subclusterPS:self_contribution_c) 22
## cor(subclusterConc_in,subclusterPS:self_contribution_c) 26
## cor(subclusterEM,subclusterPS:self_contribution_c) 11
## cor(subclusterPS,subclusterPS:self_contribution_c) 16
## cor(subclusterSS,subclusterPS:self_contribution_c) 7
## cor(self_contribution_c,subclusterPS:self_contribution_c) 174
## cor(subclusterConc_an:self_contribution_c,subclusterPS:self_contribution_c) 55
## cor(subclusterConc_in:self_contribution_c,subclusterPS:self_contribution_c) 20
## cor(subclusterEM:self_contribution_c,subclusterPS:self_contribution_c) 15
## cor(Intercept,subclusterSS:self_contribution_c) 10
## cor(subclusterConc_an,subclusterSS:self_contribution_c) 27
## cor(subclusterConc_in,subclusterSS:self_contribution_c) 27
## cor(subclusterEM,subclusterSS:self_contribution_c) 16
## cor(subclusterPS,subclusterSS:self_contribution_c) 14
## cor(subclusterSS,subclusterSS:self_contribution_c) 10
## cor(self_contribution_c,subclusterSS:self_contribution_c) 67
## cor(subclusterConc_an:self_contribution_c,subclusterSS:self_contribution_c) 76
## cor(subclusterConc_in:self_contribution_c,subclusterSS:self_contribution_c) 7
## cor(subclusterEM:self_contribution_c,subclusterSS:self_contribution_c) 20
## cor(subclusterPS:self_contribution_c,subclusterSS:self_contribution_c) 16
## Tail_ESS
## sd(Intercept) 18
## sd(subclusterConc_an) 169
## sd(subclusterConc_in) 134
## sd(subclusterEM) 131
## sd(subclusterPS) 64
## sd(subclusterSS) 62
## sd(self_contribution_c) 170
## sd(subclusterConc_an:self_contribution_c) 95
## sd(subclusterConc_in:self_contribution_c) 117
## sd(subclusterEM:self_contribution_c) 24
## sd(subclusterPS:self_contribution_c) 28
## sd(subclusterSS:self_contribution_c) 49
## cor(Intercept,subclusterConc_an) 44
## cor(Intercept,subclusterConc_in) 123
## cor(subclusterConc_an,subclusterConc_in) 59
## cor(Intercept,subclusterEM) 140
## cor(subclusterConc_an,subclusterEM) 107
## cor(subclusterConc_in,subclusterEM) 68
## cor(Intercept,subclusterPS) 128
## cor(subclusterConc_an,subclusterPS) 127
## cor(subclusterConc_in,subclusterPS) 57
## cor(subclusterEM,subclusterPS) 18
## cor(Intercept,subclusterSS) 75
## cor(subclusterConc_an,subclusterSS) 34
## cor(subclusterConc_in,subclusterSS) 106
## cor(subclusterEM,subclusterSS) 54
## cor(subclusterPS,subclusterSS) 18
## cor(Intercept,self_contribution_c) 180
## cor(subclusterConc_an,self_contribution_c) 26
## cor(subclusterConc_in,self_contribution_c) 36
## cor(subclusterEM,self_contribution_c) 86
## cor(subclusterPS,self_contribution_c) 161
## cor(subclusterSS,self_contribution_c) 140
## cor(Intercept,subclusterConc_an:self_contribution_c) 197
## cor(subclusterConc_an,subclusterConc_an:self_contribution_c) 112
## cor(subclusterConc_in,subclusterConc_an:self_contribution_c) 46
## cor(subclusterEM,subclusterConc_an:self_contribution_c) 367
## cor(subclusterPS,subclusterConc_an:self_contribution_c) 52
## cor(subclusterSS,subclusterConc_an:self_contribution_c) 54
## cor(self_contribution_c,subclusterConc_an:self_contribution_c) 57
## cor(Intercept,subclusterConc_in:self_contribution_c) 198
## cor(subclusterConc_an,subclusterConc_in:self_contribution_c) 427
## cor(subclusterConc_in,subclusterConc_in:self_contribution_c) 243
## cor(subclusterEM,subclusterConc_in:self_contribution_c) 37
## cor(subclusterPS,subclusterConc_in:self_contribution_c) 63
## cor(subclusterSS,subclusterConc_in:self_contribution_c) 186
## cor(self_contribution_c,subclusterConc_in:self_contribution_c) 244
## cor(subclusterConc_an:self_contribution_c,subclusterConc_in:self_contribution_c) 386
## cor(Intercept,subclusterEM:self_contribution_c) 401
## cor(subclusterConc_an,subclusterEM:self_contribution_c) 21
## cor(subclusterConc_in,subclusterEM:self_contribution_c) 14
## cor(subclusterEM,subclusterEM:self_contribution_c) 293
## cor(subclusterPS,subclusterEM:self_contribution_c) 137
## cor(subclusterSS,subclusterEM:self_contribution_c) 87
## cor(self_contribution_c,subclusterEM:self_contribution_c) 52
## cor(subclusterConc_an:self_contribution_c,subclusterEM:self_contribution_c) 155
## cor(subclusterConc_in:self_contribution_c,subclusterEM:self_contribution_c) 439
## cor(Intercept,subclusterPS:self_contribution_c) 214
## cor(subclusterConc_an,subclusterPS:self_contribution_c) 119
## cor(subclusterConc_in,subclusterPS:self_contribution_c) 112
## cor(subclusterEM,subclusterPS:self_contribution_c) 43
## cor(subclusterPS,subclusterPS:self_contribution_c) 89
## cor(subclusterSS,subclusterPS:self_contribution_c) 20
## cor(self_contribution_c,subclusterPS:self_contribution_c) 282
## cor(subclusterConc_an:self_contribution_c,subclusterPS:self_contribution_c) 56
## cor(subclusterConc_in:self_contribution_c,subclusterPS:self_contribution_c) 99
## cor(subclusterEM:self_contribution_c,subclusterPS:self_contribution_c) 162
## cor(Intercept,subclusterSS:self_contribution_c) 56
## cor(subclusterConc_an,subclusterSS:self_contribution_c) 220
## cor(subclusterConc_in,subclusterSS:self_contribution_c) 143
## cor(subclusterEM,subclusterSS:self_contribution_c) 81
## cor(subclusterPS,subclusterSS:self_contribution_c) 154
## cor(subclusterSS,subclusterSS:self_contribution_c) 102
## cor(self_contribution_c,subclusterSS:self_contribution_c) 152
## cor(subclusterConc_an:self_contribution_c,subclusterSS:self_contribution_c) 151
## cor(subclusterConc_in:self_contribution_c,subclusterSS:self_contribution_c) 44
## cor(subclusterEM:self_contribution_c,subclusterSS:self_contribution_c) 109
## cor(subclusterPS:self_contribution_c,subclusterSS:self_contribution_c) 126
##
## ~word (Number of levels: 32)
## Estimate Est.Error l-95% CI u-95% CI Rhat
## sd(Intercept) 0.05 0.02 0.01 0.10 1.19
## sd(self_contribution_c) 0.00 0.00 0.00 0.01 1.43
## cor(Intercept,self_contribution_c) 0.11 0.59 -0.99 0.95 1.70
## Bulk_ESS Tail_ESS
## sd(Intercept) 16 137
## sd(self_contribution_c) 8 45
## cor(Intercept,self_contribution_c) 9 14
##
## Population-Level Effects:
## Estimate Est.Error l-95% CI u-95% CI Rhat
## Intercept 1.01 0.08 0.85 1.14 1.22
## phi_Intercept 3.39 0.31 2.93 3.90 1.43
## subclusterConc_an -0.06 0.08 -0.21 0.09 1.20
## subclusterConc_in -0.07 0.06 -0.19 0.08 1.30
## subclusterEM -0.04 0.08 -0.15 0.13 1.21
## subclusterPS -0.01 0.08 -0.18 0.18 1.40
## subclusterSS -0.04 0.06 -0.16 0.09 1.37
## self_contribution_c 0.01 0.00 0.01 0.02 1.32
## difficulty_c -0.01 0.00 -0.01 -0.01 1.23
## subclusterConc_an:self_contribution_c -0.00 0.00 -0.01 0.00 1.23
## subclusterConc_in:self_contribution_c -0.00 0.00 -0.01 0.00 1.30
## subclusterEM:self_contribution_c -0.00 0.00 -0.01 0.00 1.22
## subclusterPS:self_contribution_c -0.00 0.01 -0.01 0.00 1.41
## subclusterSS:self_contribution_c -0.01 0.00 -0.01 0.00 1.29
## phi_subclusterConc_an -0.04 0.28 -0.49 0.45 1.30
## phi_subclusterConc_in 0.23 0.32 -0.25 0.76 1.38
## phi_subclusterEM 0.63 0.40 0.07 1.39 1.42
## phi_subclusterPS 0.89 1.05 -0.55 2.62 1.74
## phi_subclusterSS 9.04 5.54 1.06 16.71 2.25
## Bulk_ESS Tail_ESS
## Intercept 14 139
## phi_Intercept 9 95
## subclusterConc_an 15 63
## subclusterConc_in 25 121
## subclusterEM 13 61
## subclusterPS 15 22
## subclusterSS 52 171
## self_contribution_c 23 125
## difficulty_c 33 161
## subclusterConc_an:self_contribution_c 64 170
## subclusterConc_in:self_contribution_c 190 128
## subclusterEM:self_contribution_c 33 118
## subclusterPS:self_contribution_c 8 24
## subclusterSS:self_contribution_c 11 143
## phi_subclusterConc_an 11 155
## phi_subclusterConc_in 9 70
## phi_subclusterEM 8 94
## phi_subclusterPS 6 37
## phi_subclusterSS 5 17
##
## Draws were sampled using sampling(NUTS). For each parameter, Bulk_ESS
## and Tail_ESS are effective sample size measures, and Rhat is the potential
## scale reduction factor on split chains (at convergence, Rhat = 1).Perform hypothesis tests on the fixed effects coefficient:
hypothesis(subcluster_dist_self_mdl,
'difficulty_c < 0')## Hypothesis Tests for class b:
## Hypothesis Estimate Est.Error CI.Lower CI.Upper Evid.Ratio Post.Prob
## 1 (difficulty_c) < 0 -0.01 0 -0.01 -0.01 Inf 1
## Star
## 1 *
## ---
## 'CI': 90%-CI for one-sided and 95%-CI for two-sided hypotheses.
## '*': For one-sided hypotheses, the posterior probability exceeds 95%;
## for two-sided hypotheses, the value tested against lies outside the 95%-CI.
## Posterior probabilities of point hypotheses assume equal prior probabilities.hypothesis(subcluster_dist_self_mdl,
'self_contribution_c > 0')## Hypothesis Tests for class b:
## Hypothesis Estimate Est.Error CI.Lower CI.Upper Evid.Ratio
## 1 (self_contributio... > 0 0.01 0 0.01 0.02 5999
## Post.Prob Star
## 1 1 *
## ---
## 'CI': 90%-CI for one-sided and 95%-CI for two-sided hypotheses.
## '*': For one-sided hypotheses, the posterior probability exceeds 95%;
## for two-sided hypotheses, the value tested against lies outside the 95%-CI.
## Posterior probabilities of point hypotheses assume equal prior probabilities.hypothesis(subcluster_dist_self_mdl,
'subclusterConc_an:self_contribution_c < 0') # PSTQ is reference## Hypothesis Tests for class b:
## Hypothesis Estimate Est.Error CI.Lower CI.Upper Evid.Ratio
## 1 (subclusterConc_a... < 0 0 0 -0.01 0 9.64
## Post.Prob Star
## 1 0.91
## ---
## 'CI': 90%-CI for one-sided and 95%-CI for two-sided hypotheses.
## '*': For one-sided hypotheses, the posterior probability exceeds 95%;
## for two-sided hypotheses, the value tested against lies outside the 95%-CI.
## Posterior probabilities of point hypotheses assume equal prior probabilities.hypothesis(subcluster_dist_self_mdl,
'subclusterConc_in:self_contribution_c < 0') # PSTQ is reference## Hypothesis Tests for class b:
## Hypothesis Estimate Est.Error CI.Lower CI.Upper Evid.Ratio
## 1 (subclusterConc_i... < 0 0 0 -0.01 0 6.27
## Post.Prob Star
## 1 0.86
## ---
## 'CI': 90%-CI for one-sided and 95%-CI for two-sided hypotheses.
## '*': For one-sided hypotheses, the posterior probability exceeds 95%;
## for two-sided hypotheses, the value tested against lies outside the 95%-CI.
## Posterior probabilities of point hypotheses assume equal prior probabilities.hypothesis(subcluster_dist_self_mdl,
'subclusterEM:self_contribution_c < 0') # PSTQ is reference## Hypothesis Tests for class b:
## Hypothesis Estimate Est.Error CI.Lower CI.Upper Evid.Ratio
## 1 (subclusterEM:sel... < 0 0 0 -0.01 0 4.39
## Post.Prob Star
## 1 0.81
## ---
## 'CI': 90%-CI for one-sided and 95%-CI for two-sided hypotheses.
## '*': For one-sided hypotheses, the posterior probability exceeds 95%;
## for two-sided hypotheses, the value tested against lies outside the 95%-CI.
## Posterior probabilities of point hypotheses assume equal prior probabilities.hypothesis(subcluster_dist_self_mdl,
'subclusterPS:self_contribution_c < 0') # PSTQ is reference## Hypothesis Tests for class b:
## Hypothesis Estimate Est.Error CI.Lower CI.Upper Evid.Ratio
## 1 (subclusterPS:sel... < 0 0 0.01 -0.01 0 2.13
## Post.Prob Star
## 1 0.68
## ---
## 'CI': 90%-CI for one-sided and 95%-CI for two-sided hypotheses.
## '*': For one-sided hypotheses, the posterior probability exceeds 95%;
## for two-sided hypotheses, the value tested against lies outside the 95%-CI.
## Posterior probabilities of point hypotheses assume equal prior probabilities.hypothesis(subcluster_dist_self_mdl,
'subclusterSS:self_contribution_c < 0') # PSTQ is reference## Hypothesis Tests for class b:
## Hypothesis Estimate Est.Error CI.Lower CI.Upper Evid.Ratio
## 1 (subclusterSS:sel... < 0 -0.01 0 -0.01 0 15.64
## Post.Prob Star
## 1 0.94
## ---
## 'CI': 90%-CI for one-sided and 95%-CI for two-sided hypotheses.
## '*': For one-sided hypotheses, the posterior probability exceeds 95%;
## for two-sided hypotheses, the value tested against lies outside the 95%-CI.
## Posterior probabilities of point hypotheses assume equal prior probabilities.15 Subcluster analysis of abstract concepts only
Let’s perform models just focusing on the abstract concepts only, since the hypothesis about the different subclusters is really only about abstract concepts.
IOS_subset_other_mdl <- brm(IOS ~
# Fixed effects:
1 +
subcluster +
other_contribution_c +
difficulty_c +
subcluster:other_contribution_c +
# Random effects:
(1 +
subcluster +
other_contribution_c +
subcluster:other_contribution_c|participant) +
(1 + other_contribution_c|word),
data = filter(df, category == 'abstract'),
family = cumulative,
# MCMC settings:
seed = 42,
cores = 4,
iter = 6000,
warmup = 3000,
save_pars = save_pars(all = TRUE), # for bayes factors
control = list(adapt_delta = 0.99))
# Save model:
save(IOS_subset_other_mdl,
file = '../models_E2/IOS_subset_other_mdl.Rdata')Corresponding null model:
IOS_subset_null_mdl <- brm(IOS ~
# Fixed effects:
1 +
subcluster +
other_contribution_c +
difficulty_c +
# Random effects:
(1 +
subcluster +
other_contribution_c +
subcluster:other_contribution_c|participant) +
(1 + other_contribution_c|word),
data = filter(df, category == 'abstract'),
family = cumulative,
# MCMC settings:
seed = 42,
cores = 4,
iter = 6000,
warmup = 3000,
save_pars = save_pars(all = TRUE), # for bayes factors
control = list(adapt_delta = 0.99))
# Save model:
save(IOS_subset_null_mdl,
file = '../models_E2/IOS_subset_null_mdl.Rdata')Load model:
load('../models_E2/IOS_subset_other_mdl.Rdata')
load('../models_E2/IOS_subset_null_mdl.Rdata')Show priors:
prior_summary(IOS_subset_other_mdl)## prior class coef group
## (flat) b
## (flat) b difficulty_c
## (flat) b other_contribution_c
## (flat) b subclusterEM
## (flat) b subclusterEM:other_contribution_c
## (flat) b subclusterPS
## (flat) b subclusterPS:other_contribution_c
## (flat) b subclusterSS
## (flat) b subclusterSS:other_contribution_c
## student_t(3, 0, 2.5) Intercept
## student_t(3, 0, 2.5) Intercept 1
## student_t(3, 0, 2.5) Intercept 2
## student_t(3, 0, 2.5) Intercept 3
## student_t(3, 0, 2.5) Intercept 4
## student_t(3, 0, 2.5) Intercept 5
## lkj_corr_cholesky(1) L
## lkj_corr_cholesky(1) L participant
## lkj_corr_cholesky(1) L word
## student_t(3, 0, 2.5) sd
## student_t(3, 0, 2.5) sd participant
## student_t(3, 0, 2.5) sd Intercept participant
## student_t(3, 0, 2.5) sd other_contribution_c participant
## student_t(3, 0, 2.5) sd subclusterEM participant
## student_t(3, 0, 2.5) sd subclusterEM:other_contribution_c participant
## student_t(3, 0, 2.5) sd subclusterPS participant
## student_t(3, 0, 2.5) sd subclusterPS:other_contribution_c participant
## student_t(3, 0, 2.5) sd subclusterSS participant
## student_t(3, 0, 2.5) sd subclusterSS:other_contribution_c participant
## student_t(3, 0, 2.5) sd word
## student_t(3, 0, 2.5) sd Intercept word
## student_t(3, 0, 2.5) sd other_contribution_c word
## resp dpar nlpar lb ub source
## default
## (vectorized)
## (vectorized)
## (vectorized)
## (vectorized)
## (vectorized)
## (vectorized)
## (vectorized)
## (vectorized)
## default
## (vectorized)
## (vectorized)
## (vectorized)
## (vectorized)
## (vectorized)
## default
## (vectorized)
## (vectorized)
## 0 default
## 0 (vectorized)
## 0 (vectorized)
## 0 (vectorized)
## 0 (vectorized)
## 0 (vectorized)
## 0 (vectorized)
## 0 (vectorized)
## 0 (vectorized)
## 0 (vectorized)
## 0 (vectorized)
## 0 (vectorized)
## 0 (vectorized)prior_summary(IOS_subset_null_mdl)## prior class coef group
## (flat) b
## (flat) b difficulty_c
## (flat) b other_contribution_c
## (flat) b subclusterEM
## (flat) b subclusterPS
## (flat) b subclusterSS
## student_t(3, 0, 2.5) Intercept
## student_t(3, 0, 2.5) Intercept 1
## student_t(3, 0, 2.5) Intercept 2
## student_t(3, 0, 2.5) Intercept 3
## student_t(3, 0, 2.5) Intercept 4
## student_t(3, 0, 2.5) Intercept 5
## lkj_corr_cholesky(1) L
## lkj_corr_cholesky(1) L participant
## lkj_corr_cholesky(1) L word
## student_t(3, 0, 2.5) sd
## student_t(3, 0, 2.5) sd participant
## student_t(3, 0, 2.5) sd Intercept participant
## student_t(3, 0, 2.5) sd other_contribution_c participant
## student_t(3, 0, 2.5) sd subclusterEM participant
## student_t(3, 0, 2.5) sd subclusterEM:other_contribution_c participant
## student_t(3, 0, 2.5) sd subclusterPS participant
## student_t(3, 0, 2.5) sd subclusterPS:other_contribution_c participant
## student_t(3, 0, 2.5) sd subclusterSS participant
## student_t(3, 0, 2.5) sd subclusterSS:other_contribution_c participant
## student_t(3, 0, 2.5) sd word
## student_t(3, 0, 2.5) sd Intercept word
## student_t(3, 0, 2.5) sd other_contribution_c word
## resp dpar nlpar lb ub source
## default
## (vectorized)
## (vectorized)
## (vectorized)
## (vectorized)
## (vectorized)
## default
## (vectorized)
## (vectorized)
## (vectorized)
## (vectorized)
## (vectorized)
## default
## (vectorized)
## (vectorized)
## 0 default
## 0 (vectorized)
## 0 (vectorized)
## 0 (vectorized)
## 0 (vectorized)
## 0 (vectorized)
## 0 (vectorized)
## 0 (vectorized)
## 0 (vectorized)
## 0 (vectorized)
## 0 (vectorized)
## 0 (vectorized)
## 0 (vectorized)Bayes factors for both:
# Compute Bayes factor:
IOS_subset_bf <- bayes_factor(IOS_subset_other_mdl, IOS_subset_null_mdl)
# Save:
save(IOS_subset_bf,
file = '../models_E2/IOS_subset_bf.RData')Show Bayes factor:
# Load:
load('../models_E2/IOS_subset_bf.RData')
# Show:
IOS_subset_bf## Estimated Bayes factor in favor of IOS_subset_other_mdl over IOS_subset_null_mdl: 0.00000Check posterior predictive checks of the mixed beta regression:
pp_check(IOS_subset_other_mdl, ndraws = 100)
Check this model:
IOS_subset_other_mdl## Family: cumulative
## Links: mu = logit; disc = identity
## Formula: IOS ~ 1 + subcluster + other_contribution_c + difficulty_c + subcluster:other_contribution_c + (1 + subcluster + other_contribution_c + subcluster:other_contribution_c | participant) + (1 + other_contribution_c | word)
## Data: filter(df, category == "abstract") (Number of observations: 516)
## Draws: 4 chains, each with iter = 6000; warmup = 3000; thin = 1;
## total post-warmup draws = 12000
##
## Group-Level Effects:
## ~participant (Number of levels: 129)
## Estimate
## sd(Intercept) 3.03
## sd(subclusterEM) 0.60
## sd(subclusterPS) 0.51
## sd(subclusterSS) 0.83
## sd(other_contribution_c) 0.07
## sd(subclusterEM:other_contribution_c) 0.06
## sd(subclusterPS:other_contribution_c) 0.04
## sd(subclusterSS:other_contribution_c) 0.04
## cor(Intercept,subclusterEM) -0.05
## cor(Intercept,subclusterPS) 0.01
## cor(subclusterEM,subclusterPS) 0.05
## cor(Intercept,subclusterSS) -0.10
## cor(subclusterEM,subclusterSS) -0.00
## cor(subclusterPS,subclusterSS) -0.00
## cor(Intercept,other_contribution_c) -0.04
## cor(subclusterEM,other_contribution_c) -0.10
## cor(subclusterPS,other_contribution_c) 0.01
## cor(subclusterSS,other_contribution_c) 0.15
## cor(Intercept,subclusterEM:other_contribution_c) -0.01
## cor(subclusterEM,subclusterEM:other_contribution_c) 0.04
## cor(subclusterPS,subclusterEM:other_contribution_c) -0.11
## cor(subclusterSS,subclusterEM:other_contribution_c) 0.03
## cor(other_contribution_c,subclusterEM:other_contribution_c) -0.09
## cor(Intercept,subclusterPS:other_contribution_c) 0.19
## cor(subclusterEM,subclusterPS:other_contribution_c) -0.10
## cor(subclusterPS,subclusterPS:other_contribution_c) -0.01
## cor(subclusterSS,subclusterPS:other_contribution_c) 0.06
## cor(other_contribution_c,subclusterPS:other_contribution_c) -0.03
## cor(subclusterEM:other_contribution_c,subclusterPS:other_contribution_c) 0.01
## cor(Intercept,subclusterSS:other_contribution_c) 0.12
## cor(subclusterEM,subclusterSS:other_contribution_c) 0.02
## cor(subclusterPS,subclusterSS:other_contribution_c) 0.05
## cor(subclusterSS,subclusterSS:other_contribution_c) -0.10
## cor(other_contribution_c,subclusterSS:other_contribution_c) 0.07
## cor(subclusterEM:other_contribution_c,subclusterSS:other_contribution_c) 0.11
## cor(subclusterPS:other_contribution_c,subclusterSS:other_contribution_c) 0.10
## Est.Error
## sd(Intercept) 0.36
## sd(subclusterEM) 0.44
## sd(subclusterPS) 0.39
## sd(subclusterSS) 0.53
## sd(other_contribution_c) 0.02
## sd(subclusterEM:other_contribution_c) 0.03
## sd(subclusterPS:other_contribution_c) 0.03
## sd(subclusterSS:other_contribution_c) 0.03
## cor(Intercept,subclusterEM) 0.29
## cor(Intercept,subclusterPS) 0.30
## cor(subclusterEM,subclusterPS) 0.33
## cor(Intercept,subclusterSS) 0.28
## cor(subclusterEM,subclusterSS) 0.32
## cor(subclusterPS,subclusterSS) 0.33
## cor(Intercept,other_contribution_c) 0.20
## cor(subclusterEM,other_contribution_c) 0.32
## cor(subclusterPS,other_contribution_c) 0.32
## cor(subclusterSS,other_contribution_c) 0.31
## cor(Intercept,subclusterEM:other_contribution_c) 0.25
## cor(subclusterEM,subclusterEM:other_contribution_c) 0.33
## cor(subclusterPS,subclusterEM:other_contribution_c) 0.33
## cor(subclusterSS,subclusterEM:other_contribution_c) 0.32
## cor(other_contribution_c,subclusterEM:other_contribution_c) 0.30
## cor(Intercept,subclusterPS:other_contribution_c) 0.28
## cor(subclusterEM,subclusterPS:other_contribution_c) 0.33
## cor(subclusterPS,subclusterPS:other_contribution_c) 0.33
## cor(subclusterSS,subclusterPS:other_contribution_c) 0.33
## cor(other_contribution_c,subclusterPS:other_contribution_c) 0.31
## cor(subclusterEM:other_contribution_c,subclusterPS:other_contribution_c) 0.31
## cor(Intercept,subclusterSS:other_contribution_c) 0.30
## cor(subclusterEM,subclusterSS:other_contribution_c) 0.33
## cor(subclusterPS,subclusterSS:other_contribution_c) 0.33
## cor(subclusterSS,subclusterSS:other_contribution_c) 0.33
## cor(other_contribution_c,subclusterSS:other_contribution_c) 0.32
## cor(subclusterEM:other_contribution_c,subclusterSS:other_contribution_c) 0.32
## cor(subclusterPS:other_contribution_c,subclusterSS:other_contribution_c) 0.33
## l-95% CI
## sd(Intercept) 2.39
## sd(subclusterEM) 0.02
## sd(subclusterPS) 0.02
## sd(subclusterSS) 0.04
## sd(other_contribution_c) 0.02
## sd(subclusterEM:other_contribution_c) 0.01
## sd(subclusterPS:other_contribution_c) 0.00
## sd(subclusterSS:other_contribution_c) 0.00
## cor(Intercept,subclusterEM) -0.58
## cor(Intercept,subclusterPS) -0.58
## cor(subclusterEM,subclusterPS) -0.59
## cor(Intercept,subclusterSS) -0.62
## cor(subclusterEM,subclusterSS) -0.63
## cor(subclusterPS,subclusterSS) -0.63
## cor(Intercept,other_contribution_c) -0.42
## cor(subclusterEM,other_contribution_c) -0.68
## cor(subclusterPS,other_contribution_c) -0.61
## cor(subclusterSS,other_contribution_c) -0.49
## cor(Intercept,subclusterEM:other_contribution_c) -0.50
## cor(subclusterEM,subclusterEM:other_contribution_c) -0.60
## cor(subclusterPS,subclusterEM:other_contribution_c) -0.70
## cor(subclusterSS,subclusterEM:other_contribution_c) -0.60
## cor(other_contribution_c,subclusterEM:other_contribution_c) -0.61
## cor(Intercept,subclusterPS:other_contribution_c) -0.41
## cor(subclusterEM,subclusterPS:other_contribution_c) -0.70
## cor(subclusterPS,subclusterPS:other_contribution_c) -0.62
## cor(subclusterSS,subclusterPS:other_contribution_c) -0.57
## cor(other_contribution_c,subclusterPS:other_contribution_c) -0.61
## cor(subclusterEM:other_contribution_c,subclusterPS:other_contribution_c) -0.59
## cor(Intercept,subclusterSS:other_contribution_c) -0.50
## cor(subclusterEM,subclusterSS:other_contribution_c) -0.61
## cor(subclusterPS,subclusterSS:other_contribution_c) -0.59
## cor(subclusterSS,subclusterSS:other_contribution_c) -0.70
## cor(other_contribution_c,subclusterSS:other_contribution_c) -0.56
## cor(subclusterEM:other_contribution_c,subclusterSS:other_contribution_c) -0.55
## cor(subclusterPS:other_contribution_c,subclusterSS:other_contribution_c) -0.56
## u-95% CI
## sd(Intercept) 3.80
## sd(subclusterEM) 1.64
## sd(subclusterPS) 1.45
## sd(subclusterSS) 1.96
## sd(other_contribution_c) 0.11
## sd(subclusterEM:other_contribution_c) 0.11
## sd(subclusterPS:other_contribution_c) 0.11
## sd(subclusterSS:other_contribution_c) 0.11
## cor(Intercept,subclusterEM) 0.52
## cor(Intercept,subclusterPS) 0.60
## cor(subclusterEM,subclusterPS) 0.66
## cor(Intercept,subclusterSS) 0.49
## cor(subclusterEM,subclusterSS) 0.62
## cor(subclusterPS,subclusterSS) 0.62
## cor(Intercept,other_contribution_c) 0.37
## cor(subclusterEM,other_contribution_c) 0.56
## cor(subclusterPS,other_contribution_c) 0.62
## cor(subclusterSS,other_contribution_c) 0.70
## cor(Intercept,subclusterEM:other_contribution_c) 0.48
## cor(subclusterEM,subclusterEM:other_contribution_c) 0.65
## cor(subclusterPS,subclusterEM:other_contribution_c) 0.56
## cor(subclusterSS,subclusterEM:other_contribution_c) 0.63
## cor(other_contribution_c,subclusterEM:other_contribution_c) 0.52
## cor(Intercept,subclusterPS:other_contribution_c) 0.67
## cor(subclusterEM,subclusterPS:other_contribution_c) 0.57
## cor(subclusterPS,subclusterPS:other_contribution_c) 0.62
## cor(subclusterSS,subclusterPS:other_contribution_c) 0.66
## cor(other_contribution_c,subclusterPS:other_contribution_c) 0.59
## cor(subclusterEM:other_contribution_c,subclusterPS:other_contribution_c) 0.60
## cor(Intercept,subclusterSS:other_contribution_c) 0.66
## cor(subclusterEM,subclusterSS:other_contribution_c) 0.65
## cor(subclusterPS,subclusterSS:other_contribution_c) 0.67
## cor(subclusterSS,subclusterSS:other_contribution_c) 0.55
## cor(other_contribution_c,subclusterSS:other_contribution_c) 0.67
## cor(subclusterEM:other_contribution_c,subclusterSS:other_contribution_c) 0.68
## cor(subclusterPS:other_contribution_c,subclusterSS:other_contribution_c) 0.68
## Rhat
## sd(Intercept) 1.00
## sd(subclusterEM) 1.00
## sd(subclusterPS) 1.00
## sd(subclusterSS) 1.00
## sd(other_contribution_c) 1.00
## sd(subclusterEM:other_contribution_c) 1.00
## sd(subclusterPS:other_contribution_c) 1.00
## sd(subclusterSS:other_contribution_c) 1.00
## cor(Intercept,subclusterEM) 1.00
## cor(Intercept,subclusterPS) 1.00
## cor(subclusterEM,subclusterPS) 1.00
## cor(Intercept,subclusterSS) 1.00
## cor(subclusterEM,subclusterSS) 1.00
## cor(subclusterPS,subclusterSS) 1.00
## cor(Intercept,other_contribution_c) 1.00
## cor(subclusterEM,other_contribution_c) 1.00
## cor(subclusterPS,other_contribution_c) 1.00
## cor(subclusterSS,other_contribution_c) 1.00
## cor(Intercept,subclusterEM:other_contribution_c) 1.00
## cor(subclusterEM,subclusterEM:other_contribution_c) 1.00
## cor(subclusterPS,subclusterEM:other_contribution_c) 1.00
## cor(subclusterSS,subclusterEM:other_contribution_c) 1.00
## cor(other_contribution_c,subclusterEM:other_contribution_c) 1.00
## cor(Intercept,subclusterPS:other_contribution_c) 1.00
## cor(subclusterEM,subclusterPS:other_contribution_c) 1.00
## cor(subclusterPS,subclusterPS:other_contribution_c) 1.00
## cor(subclusterSS,subclusterPS:other_contribution_c) 1.00
## cor(other_contribution_c,subclusterPS:other_contribution_c) 1.00
## cor(subclusterEM:other_contribution_c,subclusterPS:other_contribution_c) 1.00
## cor(Intercept,subclusterSS:other_contribution_c) 1.00
## cor(subclusterEM,subclusterSS:other_contribution_c) 1.00
## cor(subclusterPS,subclusterSS:other_contribution_c) 1.00
## cor(subclusterSS,subclusterSS:other_contribution_c) 1.00
## cor(other_contribution_c,subclusterSS:other_contribution_c) 1.00
## cor(subclusterEM:other_contribution_c,subclusterSS:other_contribution_c) 1.00
## cor(subclusterPS:other_contribution_c,subclusterSS:other_contribution_c) 1.00
## Bulk_ESS
## sd(Intercept) 1818
## sd(subclusterEM) 1564
## sd(subclusterPS) 2120
## sd(subclusterSS) 1698
## sd(other_contribution_c) 1449
## sd(subclusterEM:other_contribution_c) 1469
## sd(subclusterPS:other_contribution_c) 1821
## sd(subclusterSS:other_contribution_c) 2099
## cor(Intercept,subclusterEM) 10633
## cor(Intercept,subclusterPS) 14051
## cor(subclusterEM,subclusterPS) 6581
## cor(Intercept,subclusterSS) 11480
## cor(subclusterEM,subclusterSS) 5209
## cor(subclusterPS,subclusterSS) 4938
## cor(Intercept,other_contribution_c) 6603
## cor(subclusterEM,other_contribution_c) 1470
## cor(subclusterPS,other_contribution_c) 1488
## cor(subclusterSS,other_contribution_c) 1815
## cor(Intercept,subclusterEM:other_contribution_c) 7336
## cor(subclusterEM,subclusterEM:other_contribution_c) 3126
## cor(subclusterPS,subclusterEM:other_contribution_c) 3473
## cor(subclusterSS,subclusterEM:other_contribution_c) 4037
## cor(other_contribution_c,subclusterEM:other_contribution_c) 4514
## cor(Intercept,subclusterPS:other_contribution_c) 9979
## cor(subclusterEM,subclusterPS:other_contribution_c) 4604
## cor(subclusterPS,subclusterPS:other_contribution_c) 5752
## cor(subclusterSS,subclusterPS:other_contribution_c) 6232
## cor(other_contribution_c,subclusterPS:other_contribution_c) 7841
## cor(subclusterEM:other_contribution_c,subclusterPS:other_contribution_c) 7002
## cor(Intercept,subclusterSS:other_contribution_c) 9519
## cor(subclusterEM,subclusterSS:other_contribution_c) 5357
## cor(subclusterPS,subclusterSS:other_contribution_c) 6596
## cor(subclusterSS,subclusterSS:other_contribution_c) 6333
## cor(other_contribution_c,subclusterSS:other_contribution_c) 7314
## cor(subclusterEM:other_contribution_c,subclusterSS:other_contribution_c) 7636
## cor(subclusterPS:other_contribution_c,subclusterSS:other_contribution_c) 6121
## Tail_ESS
## sd(Intercept) 4137
## sd(subclusterEM) 2671
## sd(subclusterPS) 3652
## sd(subclusterSS) 4249
## sd(other_contribution_c) 2108
## sd(subclusterEM:other_contribution_c) 2074
## sd(subclusterPS:other_contribution_c) 3718
## sd(subclusterSS:other_contribution_c) 4182
## cor(Intercept,subclusterEM) 7870
## cor(Intercept,subclusterPS) 8116
## cor(subclusterEM,subclusterPS) 8254
## cor(Intercept,subclusterSS) 7967
## cor(subclusterEM,subclusterSS) 6700
## cor(subclusterPS,subclusterSS) 8192
## cor(Intercept,other_contribution_c) 7402
## cor(subclusterEM,other_contribution_c) 3365
## cor(subclusterPS,other_contribution_c) 3578
## cor(subclusterSS,other_contribution_c) 3580
## cor(Intercept,subclusterEM:other_contribution_c) 7347
## cor(subclusterEM,subclusterEM:other_contribution_c) 6182
## cor(subclusterPS,subclusterEM:other_contribution_c) 6589
## cor(subclusterSS,subclusterEM:other_contribution_c) 7273
## cor(other_contribution_c,subclusterEM:other_contribution_c) 7826
## cor(Intercept,subclusterPS:other_contribution_c) 6866
## cor(subclusterEM,subclusterPS:other_contribution_c) 8185
## cor(subclusterPS,subclusterPS:other_contribution_c) 8167
## cor(subclusterSS,subclusterPS:other_contribution_c) 8675
## cor(other_contribution_c,subclusterPS:other_contribution_c) 9157
## cor(subclusterEM:other_contribution_c,subclusterPS:other_contribution_c) 8838
## cor(Intercept,subclusterSS:other_contribution_c) 8336
## cor(subclusterEM,subclusterSS:other_contribution_c) 8390
## cor(subclusterPS,subclusterSS:other_contribution_c) 9026
## cor(subclusterSS,subclusterSS:other_contribution_c) 8586
## cor(other_contribution_c,subclusterSS:other_contribution_c) 7682
## cor(subclusterEM:other_contribution_c,subclusterSS:other_contribution_c) 9120
## cor(subclusterPS:other_contribution_c,subclusterSS:other_contribution_c) 9647
##
## ~word (Number of levels: 16)
## Estimate Est.Error l-95% CI u-95% CI Rhat
## sd(Intercept) 0.24 0.18 0.01 0.69 1.00
## sd(other_contribution_c) 0.02 0.01 0.00 0.05 1.00
## cor(Intercept,other_contribution_c) -0.07 0.57 -0.95 0.93 1.00
## Bulk_ESS Tail_ESS
## sd(Intercept) 3998 5608
## sd(other_contribution_c) 2133 4121
## cor(Intercept,other_contribution_c) 4907 7558
##
## Population-Level Effects:
## Estimate Est.Error l-95% CI u-95% CI Rhat
## Intercept[1] -6.40 0.66 -7.79 -5.22 1.00
## Intercept[2] -2.07 0.41 -2.92 -1.30 1.00
## Intercept[3] 1.03 0.40 0.26 1.82 1.00
## Intercept[4] 3.66 0.49 2.75 4.66 1.00
## Intercept[5] 6.97 0.70 5.71 8.45 1.00
## subclusterEM 0.10 0.35 -0.59 0.79 1.00
## subclusterPS -0.02 0.36 -0.75 0.71 1.00
## subclusterSS -0.16 0.41 -0.97 0.62 1.00
## other_contribution_c 0.06 0.02 0.02 0.10 1.00
## difficulty_c -0.03 0.01 -0.05 -0.02 1.00
## subclusterEM:other_contribution_c -0.00 0.02 -0.05 0.04 1.00
## subclusterPS:other_contribution_c 0.01 0.02 -0.04 0.06 1.00
## subclusterSS:other_contribution_c 0.01 0.03 -0.05 0.06 1.00
## Bulk_ESS Tail_ESS
## Intercept[1] 2502 4652
## Intercept[2] 4068 6607
## Intercept[3] 4545 5839
## Intercept[4] 3134 4861
## Intercept[5] 2489 3839
## subclusterEM 7697 6938
## subclusterPS 8642 7728
## subclusterSS 6904 6589
## other_contribution_c 4740 5337
## difficulty_c 6602 8466
## subclusterEM:other_contribution_c 6370 5583
## subclusterPS:other_contribution_c 6021 5908
## subclusterSS:other_contribution_c 6001 6151
##
## Family Specific Parameters:
## Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
## disc 1.00 0.00 1.00 1.00 NA NA NA
##
## Draws were sampled using sampling(NUTS). For each parameter, Bulk_ESS
## and Tail_ESS are effective sample size measures, and Rhat is the potential
## scale reduction factor on split chains (at convergence, Rhat = 1).Perform hypothesis tests on the fixed effects coefficient:
hypothesis(IOS_subset_other_mdl,
'difficulty_c < 0')## Hypothesis Tests for class b:
## Hypothesis Estimate Est.Error CI.Lower CI.Upper Evid.Ratio Post.Prob
## 1 (difficulty_c) < 0 -0.03 0.01 -0.04 -0.02 Inf 1
## Star
## 1 *
## ---
## 'CI': 90%-CI for one-sided and 95%-CI for two-sided hypotheses.
## '*': For one-sided hypotheses, the posterior probability exceeds 95%;
## for two-sided hypotheses, the value tested against lies outside the 95%-CI.
## Posterior probabilities of point hypotheses assume equal prior probabilities.hypothesis(IOS_subset_other_mdl,
'other_contribution_c > 0')## Hypothesis Tests for class b:
## Hypothesis Estimate Est.Error CI.Lower CI.Upper Evid.Ratio
## 1 (other_contributi... > 0 0.06 0.02 0.03 0.09 427.57
## Post.Prob Star
## 1 1 *
## ---
## 'CI': 90%-CI for one-sided and 95%-CI for two-sided hypotheses.
## '*': For one-sided hypotheses, the posterior probability exceeds 95%;
## for two-sided hypotheses, the value tested against lies outside the 95%-CI.
## Posterior probabilities of point hypotheses assume equal prior probabilities.hypothesis(IOS_subset_other_mdl,
'subclusterEM:other_contribution_c < 0') # PSTQ is reference## Hypothesis Tests for class b:
## Hypothesis Estimate Est.Error CI.Lower CI.Upper Evid.Ratio
## 1 (subclusterEM:oth... < 0 0 0.02 -0.04 0.03 1.25
## Post.Prob Star
## 1 0.56
## ---
## 'CI': 90%-CI for one-sided and 95%-CI for two-sided hypotheses.
## '*': For one-sided hypotheses, the posterior probability exceeds 95%;
## for two-sided hypotheses, the value tested against lies outside the 95%-CI.
## Posterior probabilities of point hypotheses assume equal prior probabilities.hypothesis(IOS_subset_other_mdl,
'subclusterPS:other_contribution_c < 0') # PSTQ is reference## Hypothesis Tests for class b:
## Hypothesis Estimate Est.Error CI.Lower CI.Upper Evid.Ratio
## 1 (subclusterPS:oth... < 0 0.01 0.02 -0.03 0.05 0.43
## Post.Prob Star
## 1 0.3
## ---
## 'CI': 90%-CI for one-sided and 95%-CI for two-sided hypotheses.
## '*': For one-sided hypotheses, the posterior probability exceeds 95%;
## for two-sided hypotheses, the value tested against lies outside the 95%-CI.
## Posterior probabilities of point hypotheses assume equal prior probabilities.hypothesis(IOS_subset_other_mdl,
'subclusterSS:other_contribution_c < 0') # PSTQ is reference## Hypothesis Tests for class b:
## Hypothesis Estimate Est.Error CI.Lower CI.Upper Evid.Ratio
## 1 (subclusterSS:oth... < 0 0.01 0.03 -0.03 0.05 0.51
## Post.Prob Star
## 1 0.34
## ---
## 'CI': 90%-CI for one-sided and 95%-CI for two-sided hypotheses.
## '*': For one-sided hypotheses, the posterior probability exceeds 95%;
## for two-sided hypotheses, the value tested against lies outside the 95%-CI.
## Posterior probabilities of point hypotheses assume equal prior probabilities.Next, the model with IOS on self contribution:
IOS_subset_self_mdl <- brm(IOS ~
# Fixed effects:
1 +
subcluster +
self_contribution_c +
difficulty_c +
subcluster:self_contribution_c +
# Random effects:
(1 +
subcluster +
self_contribution_c +
subcluster:self_contribution_c|participant) +
(1 + self_contribution_c|word),
data = filter(df, category == 'abstract'),
family = cumulative,
# MCMC settings:
seed = 42,
cores = 4,
iter = 6000,
warmup = 3000,
save_pars = save_pars(all = TRUE), # for bayes factors
control = list(adapt_delta = 0.99))
# Save model:
save(IOS_subset_self_mdl,
file = '../models_E2/IOS_subset_self_mdl.Rdata')Corresponding null model:
IOS_subset_self_null <- brm(IOS ~
# Fixed effects:
1 +
subcluster +
self_contribution_c +
difficulty_c +
# Random effects:
(1 +
subcluster +
self_contribution_c +
subcluster:self_contribution_c|participant) +
(1 + self_contribution_c|word),
data = filter(df, category == 'abstract'),
family = cumulative,
# MCMC settings:
seed = 42,
cores = 4,
iter = 6000,
warmup = 3000,
save_pars = save_pars(all = TRUE), # for bayes factors
control = list(adapt_delta = 0.99))
# Save model:
save(IOS_subset_self_null,
file = '../models_E2/IOS_subset_self_null.RData')Load model:
load('../models_E2/IOS_subset_self_mdl.Rdata')
load('../models_E2/IOS_subset_self_null.RData')Show priors:
prior_summary(IOS_subset_self_mdl)## prior class coef group
## (flat) b
## (flat) b difficulty_c
## (flat) b self_contribution_c
## (flat) b subclusterEM
## (flat) b subclusterEM:self_contribution_c
## (flat) b subclusterPS
## (flat) b subclusterPS:self_contribution_c
## (flat) b subclusterSS
## (flat) b subclusterSS:self_contribution_c
## student_t(3, 0, 2.5) Intercept
## student_t(3, 0, 2.5) Intercept 1
## student_t(3, 0, 2.5) Intercept 2
## student_t(3, 0, 2.5) Intercept 3
## student_t(3, 0, 2.5) Intercept 4
## student_t(3, 0, 2.5) Intercept 5
## lkj_corr_cholesky(1) L
## lkj_corr_cholesky(1) L participant
## lkj_corr_cholesky(1) L word
## student_t(3, 0, 2.5) sd
## student_t(3, 0, 2.5) sd participant
## student_t(3, 0, 2.5) sd Intercept participant
## student_t(3, 0, 2.5) sd self_contribution_c participant
## student_t(3, 0, 2.5) sd subclusterEM participant
## student_t(3, 0, 2.5) sd subclusterEM:self_contribution_c participant
## student_t(3, 0, 2.5) sd subclusterPS participant
## student_t(3, 0, 2.5) sd subclusterPS:self_contribution_c participant
## student_t(3, 0, 2.5) sd subclusterSS participant
## student_t(3, 0, 2.5) sd subclusterSS:self_contribution_c participant
## student_t(3, 0, 2.5) sd word
## student_t(3, 0, 2.5) sd Intercept word
## student_t(3, 0, 2.5) sd self_contribution_c word
## resp dpar nlpar lb ub source
## default
## (vectorized)
## (vectorized)
## (vectorized)
## (vectorized)
## (vectorized)
## (vectorized)
## (vectorized)
## (vectorized)
## default
## (vectorized)
## (vectorized)
## (vectorized)
## (vectorized)
## (vectorized)
## default
## (vectorized)
## (vectorized)
## 0 default
## 0 (vectorized)
## 0 (vectorized)
## 0 (vectorized)
## 0 (vectorized)
## 0 (vectorized)
## 0 (vectorized)
## 0 (vectorized)
## 0 (vectorized)
## 0 (vectorized)
## 0 (vectorized)
## 0 (vectorized)
## 0 (vectorized)prior_summary(IOS_subset_self_null)## prior class coef group
## (flat) b
## (flat) b difficulty_c
## (flat) b self_contribution_c
## (flat) b subclusterEM
## (flat) b subclusterPS
## (flat) b subclusterSS
## student_t(3, 0, 2.5) Intercept
## student_t(3, 0, 2.5) Intercept 1
## student_t(3, 0, 2.5) Intercept 2
## student_t(3, 0, 2.5) Intercept 3
## student_t(3, 0, 2.5) Intercept 4
## student_t(3, 0, 2.5) Intercept 5
## lkj_corr_cholesky(1) L
## lkj_corr_cholesky(1) L participant
## lkj_corr_cholesky(1) L word
## student_t(3, 0, 2.5) sd
## student_t(3, 0, 2.5) sd participant
## student_t(3, 0, 2.5) sd Intercept participant
## student_t(3, 0, 2.5) sd self_contribution_c participant
## student_t(3, 0, 2.5) sd subclusterEM participant
## student_t(3, 0, 2.5) sd subclusterEM:self_contribution_c participant
## student_t(3, 0, 2.5) sd subclusterPS participant
## student_t(3, 0, 2.5) sd subclusterPS:self_contribution_c participant
## student_t(3, 0, 2.5) sd subclusterSS participant
## student_t(3, 0, 2.5) sd subclusterSS:self_contribution_c participant
## student_t(3, 0, 2.5) sd word
## student_t(3, 0, 2.5) sd Intercept word
## student_t(3, 0, 2.5) sd self_contribution_c word
## resp dpar nlpar lb ub source
## default
## (vectorized)
## (vectorized)
## (vectorized)
## (vectorized)
## (vectorized)
## default
## (vectorized)
## (vectorized)
## (vectorized)
## (vectorized)
## (vectorized)
## default
## (vectorized)
## (vectorized)
## 0 default
## 0 (vectorized)
## 0 (vectorized)
## 0 (vectorized)
## 0 (vectorized)
## 0 (vectorized)
## 0 (vectorized)
## 0 (vectorized)
## 0 (vectorized)
## 0 (vectorized)
## 0 (vectorized)
## 0 (vectorized)
## 0 (vectorized)Bayes factors for both:
# Compute Bayes factor:
IOS_subset_self_bf <- bayes_factor(IOS_subset_self_mdl, IOS_subset_self_null)
# Save:
save(IOS_subset_self_bf,
file = '../models_E2/IOS_subset_self_bf.RData')Show Bayes factor:
# Load:
load('../models_E2/IOS_subset_self_bf.RData')
# Show:
IOS_subset_self_bf## Estimated Bayes factor in favor of IOS_subset_self_mdl over IOS_subset_self_null: 0.00000Check posterior predictive checks of the mixed beta regression:
pp_check(IOS_subset_self_mdl, ndraws = 100)
Check this model:
IOS_subset_self_mdl## Family: cumulative
## Links: mu = logit; disc = identity
## Formula: IOS ~ 1 + subcluster + self_contribution_c + difficulty_c + subcluster:self_contribution_c + (1 + subcluster + self_contribution_c + subcluster:self_contribution_c | participant) + (1 + self_contribution_c | word)
## Data: filter(df, category == "abstract") (Number of observations: 516)
## Draws: 4 chains, each with iter = 6000; warmup = 3000; thin = 1;
## total post-warmup draws = 12000
##
## Group-Level Effects:
## ~participant (Number of levels: 129)
## Estimate
## sd(Intercept) 2.94
## sd(subclusterEM) 0.56
## sd(subclusterPS) 0.73
## sd(subclusterSS) 0.52
## sd(self_contribution_c) 0.04
## sd(subclusterEM:self_contribution_c) 0.03
## sd(subclusterPS:self_contribution_c) 0.03
## sd(subclusterSS:self_contribution_c) 0.05
## cor(Intercept,subclusterEM) -0.04
## cor(Intercept,subclusterPS) 0.04
## cor(subclusterEM,subclusterPS) 0.01
## cor(Intercept,subclusterSS) 0.03
## cor(subclusterEM,subclusterSS) 0.03
## cor(subclusterPS,subclusterSS) 0.04
## cor(Intercept,self_contribution_c) 0.19
## cor(subclusterEM,self_contribution_c) -0.01
## cor(subclusterPS,self_contribution_c) 0.05
## cor(subclusterSS,self_contribution_c) 0.07
## cor(Intercept,subclusterEM:self_contribution_c) 0.12
## cor(subclusterEM,subclusterEM:self_contribution_c) 0.07
## cor(subclusterPS,subclusterEM:self_contribution_c) -0.09
## cor(subclusterSS,subclusterEM:self_contribution_c) 0.04
## cor(self_contribution_c,subclusterEM:self_contribution_c) -0.15
## cor(Intercept,subclusterPS:self_contribution_c) 0.06
## cor(subclusterEM,subclusterPS:self_contribution_c) -0.11
## cor(subclusterPS,subclusterPS:self_contribution_c) 0.08
## cor(subclusterSS,subclusterPS:self_contribution_c) -0.01
## cor(self_contribution_c,subclusterPS:self_contribution_c) 0.02
## cor(subclusterEM:self_contribution_c,subclusterPS:self_contribution_c) 0.00
## cor(Intercept,subclusterSS:self_contribution_c) 0.09
## cor(subclusterEM,subclusterSS:self_contribution_c) 0.00
## cor(subclusterPS,subclusterSS:self_contribution_c) -0.00
## cor(subclusterSS,subclusterSS:self_contribution_c) -0.05
## cor(self_contribution_c,subclusterSS:self_contribution_c) 0.02
## cor(subclusterEM:self_contribution_c,subclusterSS:self_contribution_c) 0.01
## cor(subclusterPS:self_contribution_c,subclusterSS:self_contribution_c) 0.04
## Est.Error
## sd(Intercept) 0.33
## sd(subclusterEM) 0.40
## sd(subclusterPS) 0.51
## sd(subclusterSS) 0.39
## sd(self_contribution_c) 0.02
## sd(subclusterEM:self_contribution_c) 0.02
## sd(subclusterPS:self_contribution_c) 0.02
## sd(subclusterSS:self_contribution_c) 0.03
## cor(Intercept,subclusterEM) 0.29
## cor(Intercept,subclusterPS) 0.27
## cor(subclusterEM,subclusterPS) 0.33
## cor(Intercept,subclusterSS) 0.30
## cor(subclusterEM,subclusterSS) 0.33
## cor(subclusterPS,subclusterSS) 0.33
## cor(Intercept,self_contribution_c) 0.25
## cor(subclusterEM,self_contribution_c) 0.33
## cor(subclusterPS,self_contribution_c) 0.32
## cor(subclusterSS,self_contribution_c) 0.33
## cor(Intercept,subclusterEM:self_contribution_c) 0.30
## cor(subclusterEM,subclusterEM:self_contribution_c) 0.33
## cor(subclusterPS,subclusterEM:self_contribution_c) 0.33
## cor(subclusterSS,subclusterEM:self_contribution_c) 0.34
## cor(self_contribution_c,subclusterEM:self_contribution_c) 0.34
## cor(Intercept,subclusterPS:self_contribution_c) 0.29
## cor(subclusterEM,subclusterPS:self_contribution_c) 0.34
## cor(subclusterPS,subclusterPS:self_contribution_c) 0.33
## cor(subclusterSS,subclusterPS:self_contribution_c) 0.33
## cor(self_contribution_c,subclusterPS:self_contribution_c) 0.32
## cor(subclusterEM:self_contribution_c,subclusterPS:self_contribution_c) 0.33
## cor(Intercept,subclusterSS:self_contribution_c) 0.26
## cor(subclusterEM,subclusterSS:self_contribution_c) 0.33
## cor(subclusterPS,subclusterSS:self_contribution_c) 0.32
## cor(subclusterSS,subclusterSS:self_contribution_c) 0.33
## cor(self_contribution_c,subclusterSS:self_contribution_c) 0.32
## cor(subclusterEM:self_contribution_c,subclusterSS:self_contribution_c) 0.32
## cor(subclusterPS:self_contribution_c,subclusterSS:self_contribution_c) 0.33
## l-95% CI
## sd(Intercept) 2.36
## sd(subclusterEM) 0.02
## sd(subclusterPS) 0.03
## sd(subclusterSS) 0.02
## sd(self_contribution_c) 0.00
## sd(subclusterEM:self_contribution_c) 0.00
## sd(subclusterPS:self_contribution_c) 0.00
## sd(subclusterSS:self_contribution_c) 0.00
## cor(Intercept,subclusterEM) -0.57
## cor(Intercept,subclusterPS) -0.51
## cor(subclusterEM,subclusterPS) -0.61
## cor(Intercept,subclusterSS) -0.56
## cor(subclusterEM,subclusterSS) -0.60
## cor(subclusterPS,subclusterSS) -0.61
## cor(Intercept,self_contribution_c) -0.35
## cor(subclusterEM,self_contribution_c) -0.64
## cor(subclusterPS,self_contribution_c) -0.58
## cor(subclusterSS,self_contribution_c) -0.58
## cor(Intercept,subclusterEM:self_contribution_c) -0.49
## cor(subclusterEM,subclusterEM:self_contribution_c) -0.58
## cor(subclusterPS,subclusterEM:self_contribution_c) -0.68
## cor(subclusterSS,subclusterEM:self_contribution_c) -0.61
## cor(self_contribution_c,subclusterEM:self_contribution_c) -0.73
## cor(Intercept,subclusterPS:self_contribution_c) -0.53
## cor(subclusterEM,subclusterPS:self_contribution_c) -0.71
## cor(subclusterPS,subclusterPS:self_contribution_c) -0.56
## cor(subclusterSS,subclusterPS:self_contribution_c) -0.64
## cor(self_contribution_c,subclusterPS:self_contribution_c) -0.61
## cor(subclusterEM:self_contribution_c,subclusterPS:self_contribution_c) -0.63
## cor(Intercept,subclusterSS:self_contribution_c) -0.46
## cor(subclusterEM,subclusterSS:self_contribution_c) -0.61
## cor(subclusterPS,subclusterSS:self_contribution_c) -0.61
## cor(subclusterSS,subclusterSS:self_contribution_c) -0.66
## cor(self_contribution_c,subclusterSS:self_contribution_c) -0.59
## cor(subclusterEM:self_contribution_c,subclusterSS:self_contribution_c) -0.62
## cor(subclusterPS:self_contribution_c,subclusterSS:self_contribution_c) -0.60
## u-95% CI
## sd(Intercept) 3.63
## sd(subclusterEM) 1.48
## sd(subclusterPS) 1.87
## sd(subclusterSS) 1.46
## sd(self_contribution_c) 0.08
## sd(subclusterEM:self_contribution_c) 0.08
## sd(subclusterPS:self_contribution_c) 0.09
## sd(subclusterSS:self_contribution_c) 0.11
## cor(Intercept,subclusterEM) 0.54
## cor(Intercept,subclusterPS) 0.57
## cor(subclusterEM,subclusterPS) 0.63
## cor(Intercept,subclusterSS) 0.60
## cor(subclusterEM,subclusterSS) 0.66
## cor(subclusterPS,subclusterSS) 0.65
## cor(Intercept,self_contribution_c) 0.65
## cor(subclusterEM,self_contribution_c) 0.62
## cor(subclusterPS,self_contribution_c) 0.65
## cor(subclusterSS,self_contribution_c) 0.67
## cor(Intercept,subclusterEM:self_contribution_c) 0.66
## cor(subclusterEM,subclusterEM:self_contribution_c) 0.67
## cor(subclusterPS,subclusterEM:self_contribution_c) 0.57
## cor(subclusterSS,subclusterEM:self_contribution_c) 0.66
## cor(self_contribution_c,subclusterEM:self_contribution_c) 0.54
## cor(Intercept,subclusterPS:self_contribution_c) 0.59
## cor(subclusterEM,subclusterPS:self_contribution_c) 0.57
## cor(subclusterPS,subclusterPS:self_contribution_c) 0.68
## cor(subclusterSS,subclusterPS:self_contribution_c) 0.62
## cor(self_contribution_c,subclusterPS:self_contribution_c) 0.64
## cor(subclusterEM:self_contribution_c,subclusterPS:self_contribution_c) 0.62
## cor(Intercept,subclusterSS:self_contribution_c) 0.58
## cor(subclusterEM,subclusterSS:self_contribution_c) 0.63
## cor(subclusterPS,subclusterSS:self_contribution_c) 0.62
## cor(subclusterSS,subclusterSS:self_contribution_c) 0.60
## cor(self_contribution_c,subclusterSS:self_contribution_c) 0.63
## cor(subclusterEM:self_contribution_c,subclusterSS:self_contribution_c) 0.62
## cor(subclusterPS:self_contribution_c,subclusterSS:self_contribution_c) 0.66
## Rhat
## sd(Intercept) 1.00
## sd(subclusterEM) 1.00
## sd(subclusterPS) 1.00
## sd(subclusterSS) 1.00
## sd(self_contribution_c) 1.00
## sd(subclusterEM:self_contribution_c) 1.00
## sd(subclusterPS:self_contribution_c) 1.00
## sd(subclusterSS:self_contribution_c) 1.00
## cor(Intercept,subclusterEM) 1.00
## cor(Intercept,subclusterPS) 1.00
## cor(subclusterEM,subclusterPS) 1.00
## cor(Intercept,subclusterSS) 1.00
## cor(subclusterEM,subclusterSS) 1.00
## cor(subclusterPS,subclusterSS) 1.00
## cor(Intercept,self_contribution_c) 1.00
## cor(subclusterEM,self_contribution_c) 1.00
## cor(subclusterPS,self_contribution_c) 1.00
## cor(subclusterSS,self_contribution_c) 1.00
## cor(Intercept,subclusterEM:self_contribution_c) 1.00
## cor(subclusterEM,subclusterEM:self_contribution_c) 1.00
## cor(subclusterPS,subclusterEM:self_contribution_c) 1.00
## cor(subclusterSS,subclusterEM:self_contribution_c) 1.00
## cor(self_contribution_c,subclusterEM:self_contribution_c) 1.00
## cor(Intercept,subclusterPS:self_contribution_c) 1.00
## cor(subclusterEM,subclusterPS:self_contribution_c) 1.00
## cor(subclusterPS,subclusterPS:self_contribution_c) 1.00
## cor(subclusterSS,subclusterPS:self_contribution_c) 1.00
## cor(self_contribution_c,subclusterPS:self_contribution_c) 1.00
## cor(subclusterEM:self_contribution_c,subclusterPS:self_contribution_c) 1.00
## cor(Intercept,subclusterSS:self_contribution_c) 1.00
## cor(subclusterEM,subclusterSS:self_contribution_c) 1.00
## cor(subclusterPS,subclusterSS:self_contribution_c) 1.00
## cor(subclusterSS,subclusterSS:self_contribution_c) 1.00
## cor(self_contribution_c,subclusterSS:self_contribution_c) 1.00
## cor(subclusterEM:self_contribution_c,subclusterSS:self_contribution_c) 1.00
## cor(subclusterPS:self_contribution_c,subclusterSS:self_contribution_c) 1.00
## Bulk_ESS
## sd(Intercept) 1864
## sd(subclusterEM) 1528
## sd(subclusterPS) 1037
## sd(subclusterSS) 2368
## sd(self_contribution_c) 648
## sd(subclusterEM:self_contribution_c) 1926
## sd(subclusterPS:self_contribution_c) 1939
## sd(subclusterSS:self_contribution_c) 1765
## cor(Intercept,subclusterEM) 11517
## cor(Intercept,subclusterPS) 11296
## cor(subclusterEM,subclusterPS) 4209
## cor(Intercept,subclusterSS) 12473
## cor(subclusterEM,subclusterSS) 7046
## cor(subclusterPS,subclusterSS) 7379
## cor(Intercept,self_contribution_c) 5771
## cor(subclusterEM,self_contribution_c) 2315
## cor(subclusterPS,self_contribution_c) 2781
## cor(subclusterSS,self_contribution_c) 2488
## cor(Intercept,subclusterEM:self_contribution_c) 9657
## cor(subclusterEM,subclusterEM:self_contribution_c) 5512
## cor(subclusterPS,subclusterEM:self_contribution_c) 5253
## cor(subclusterSS,subclusterEM:self_contribution_c) 6060
## cor(self_contribution_c,subclusterEM:self_contribution_c) 4566
## cor(Intercept,subclusterPS:self_contribution_c) 10887
## cor(subclusterEM,subclusterPS:self_contribution_c) 4402
## cor(subclusterPS,subclusterPS:self_contribution_c) 5617
## cor(subclusterSS,subclusterPS:self_contribution_c) 5975
## cor(self_contribution_c,subclusterPS:self_contribution_c) 7772
## cor(subclusterEM:self_contribution_c,subclusterPS:self_contribution_c) 7191
## cor(Intercept,subclusterSS:self_contribution_c) 9499
## cor(subclusterEM,subclusterSS:self_contribution_c) 5304
## cor(subclusterPS,subclusterSS:self_contribution_c) 5620
## cor(subclusterSS,subclusterSS:self_contribution_c) 5382
## cor(self_contribution_c,subclusterSS:self_contribution_c) 5784
## cor(subclusterEM:self_contribution_c,subclusterSS:self_contribution_c) 5530
## cor(subclusterPS:self_contribution_c,subclusterSS:self_contribution_c) 6413
## Tail_ESS
## sd(Intercept) 3673
## sd(subclusterEM) 2920
## sd(subclusterPS) 2688
## sd(subclusterSS) 4026
## sd(self_contribution_c) 1307
## sd(subclusterEM:self_contribution_c) 3816
## sd(subclusterPS:self_contribution_c) 4028
## sd(subclusterSS:self_contribution_c) 3174
## cor(Intercept,subclusterEM) 7808
## cor(Intercept,subclusterPS) 8539
## cor(subclusterEM,subclusterPS) 7310
## cor(Intercept,subclusterSS) 8335
## cor(subclusterEM,subclusterSS) 7962
## cor(subclusterPS,subclusterSS) 8497
## cor(Intercept,self_contribution_c) 5735
## cor(subclusterEM,self_contribution_c) 4206
## cor(subclusterPS,self_contribution_c) 4941
## cor(subclusterSS,self_contribution_c) 5246
## cor(Intercept,subclusterEM:self_contribution_c) 8015
## cor(subclusterEM,subclusterEM:self_contribution_c) 8099
## cor(subclusterPS,subclusterEM:self_contribution_c) 7472
## cor(subclusterSS,subclusterEM:self_contribution_c) 8529
## cor(self_contribution_c,subclusterEM:self_contribution_c) 7625
## cor(Intercept,subclusterPS:self_contribution_c) 7556
## cor(subclusterEM,subclusterPS:self_contribution_c) 7675
## cor(subclusterPS,subclusterPS:self_contribution_c) 8215
## cor(subclusterSS,subclusterPS:self_contribution_c) 8550
## cor(self_contribution_c,subclusterPS:self_contribution_c) 9205
## cor(subclusterEM:self_contribution_c,subclusterPS:self_contribution_c) 9946
## cor(Intercept,subclusterSS:self_contribution_c) 7399
## cor(subclusterEM,subclusterSS:self_contribution_c) 8153
## cor(subclusterPS,subclusterSS:self_contribution_c) 7956
## cor(subclusterSS,subclusterSS:self_contribution_c) 8706
## cor(self_contribution_c,subclusterSS:self_contribution_c) 8391
## cor(subclusterEM:self_contribution_c,subclusterSS:self_contribution_c) 9014
## cor(subclusterPS:self_contribution_c,subclusterSS:self_contribution_c) 9236
##
## ~word (Number of levels: 16)
## Estimate Est.Error l-95% CI u-95% CI Rhat
## sd(Intercept) 0.20 0.16 0.01 0.59 1.00
## sd(self_contribution_c) 0.01 0.01 0.00 0.04 1.00
## cor(Intercept,self_contribution_c) 0.05 0.58 -0.94 0.96 1.00
## Bulk_ESS Tail_ESS
## sd(Intercept) 3709 4927
## sd(self_contribution_c) 3750 5506
## cor(Intercept,self_contribution_c) 5917 7149
##
## Population-Level Effects:
## Estimate Est.Error l-95% CI u-95% CI Rhat
## Intercept[1] -5.89 0.57 -7.10 -4.85 1.00
## Intercept[2] -1.99 0.39 -2.77 -1.25 1.00
## Intercept[3] 0.90 0.37 0.17 1.64 1.00
## Intercept[4] 3.33 0.44 2.51 4.23 1.00
## Intercept[5] 6.39 0.63 5.25 7.73 1.00
## subclusterEM 0.19 0.31 -0.42 0.82 1.00
## subclusterPS -0.15 0.33 -0.83 0.50 1.00
## subclusterSS -0.21 0.37 -0.95 0.50 1.00
## self_contribution_c 0.05 0.02 0.02 0.08 1.00
## difficulty_c -0.03 0.01 -0.04 -0.02 1.00
## subclusterEM:self_contribution_c 0.00 0.02 -0.03 0.04 1.00
## subclusterPS:self_contribution_c -0.01 0.02 -0.05 0.02 1.00
## subclusterSS:self_contribution_c -0.01 0.02 -0.05 0.03 1.00
## Bulk_ESS Tail_ESS
## Intercept[1] 2068 3505
## Intercept[2] 3008 5389
## Intercept[3] 3586 5811
## Intercept[4] 2752 4473
## Intercept[5] 2093 3827
## subclusterEM 7493 7629
## subclusterPS 6814 6820
## subclusterSS 7314 7038
## self_contribution_c 3414 4673
## difficulty_c 5799 6579
## subclusterEM:self_contribution_c 5913 6703
## subclusterPS:self_contribution_c 5466 6859
## subclusterSS:self_contribution_c 5966 7099
##
## Family Specific Parameters:
## Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
## disc 1.00 0.00 1.00 1.00 NA NA NA
##
## Draws were sampled using sampling(NUTS). For each parameter, Bulk_ESS
## and Tail_ESS are effective sample size measures, and Rhat is the potential
## scale reduction factor on split chains (at convergence, Rhat = 1).Perform hypothesis tests on the fixed effects coefficient:
hypothesis(IOS_subset_self_mdl,
'difficulty_c < 0')## Hypothesis Tests for class b:
## Hypothesis Estimate Est.Error CI.Lower CI.Upper Evid.Ratio Post.Prob
## 1 (difficulty_c) < 0 -0.03 0.01 -0.04 -0.02 Inf 1
## Star
## 1 *
## ---
## 'CI': 90%-CI for one-sided and 95%-CI for two-sided hypotheses.
## '*': For one-sided hypotheses, the posterior probability exceeds 95%;
## for two-sided hypotheses, the value tested against lies outside the 95%-CI.
## Posterior probabilities of point hypotheses assume equal prior probabilities.hypothesis(IOS_subset_self_mdl,
'self_contribution_c > 0')## Hypothesis Tests for class b:
## Hypothesis Estimate Est.Error CI.Lower CI.Upper Evid.Ratio
## 1 (self_contributio... > 0 0.05 0.02 0.03 0.08 922.08
## Post.Prob Star
## 1 1 *
## ---
## 'CI': 90%-CI for one-sided and 95%-CI for two-sided hypotheses.
## '*': For one-sided hypotheses, the posterior probability exceeds 95%;
## for two-sided hypotheses, the value tested against lies outside the 95%-CI.
## Posterior probabilities of point hypotheses assume equal prior probabilities.hypothesis(IOS_subset_self_mdl,
'subclusterEM:self_contribution_c < 0') # PSTQ is reference## Hypothesis Tests for class b:
## Hypothesis Estimate Est.Error CI.Lower CI.Upper Evid.Ratio
## 1 (subclusterEM:sel... < 0 0 0.02 -0.03 0.03 0.83
## Post.Prob Star
## 1 0.45
## ---
## 'CI': 90%-CI for one-sided and 95%-CI for two-sided hypotheses.
## '*': For one-sided hypotheses, the posterior probability exceeds 95%;
## for two-sided hypotheses, the value tested against lies outside the 95%-CI.
## Posterior probabilities of point hypotheses assume equal prior probabilities.hypothesis(IOS_subset_self_mdl,
'subclusterPS:self_contribution_c < 0') # PSTQ is reference## Hypothesis Tests for class b:
## Hypothesis Estimate Est.Error CI.Lower CI.Upper Evid.Ratio
## 1 (subclusterPS:sel... < 0 -0.01 0.02 -0.05 0.02 3.73
## Post.Prob Star
## 1 0.79
## ---
## 'CI': 90%-CI for one-sided and 95%-CI for two-sided hypotheses.
## '*': For one-sided hypotheses, the posterior probability exceeds 95%;
## for two-sided hypotheses, the value tested against lies outside the 95%-CI.
## Posterior probabilities of point hypotheses assume equal prior probabilities.hypothesis(IOS_subset_self_mdl,
'subclusterSS:self_contribution_c < 0') # PSTQ is reference## Hypothesis Tests for class b:
## Hypothesis Estimate Est.Error CI.Lower CI.Upper Evid.Ratio
## 1 (subclusterSS:sel... < 0 -0.01 0.02 -0.04 0.03 1.82
## Post.Prob Star
## 1 0.65
## ---
## 'CI': 90%-CI for one-sided and 95%-CI for two-sided hypotheses.
## '*': For one-sided hypotheses, the posterior probability exceeds 95%;
## for two-sided hypotheses, the value tested against lies outside the 95%-CI.
## Posterior probabilities of point hypotheses assume equal prior probabilities.Next, the distance on other model for only the abstract concepts.
dist_subset_other_mdl <- brm(bf(closeness_01 ~
# Fixed effects:
1 +
subcluster +
other_contribution_c +
difficulty_c +
subcluster:other_contribution_c +
# Random effects:
(1 +
subcluster +
other_contribution_c +
subcluster:other_contribution_c|participant) +
(1 + other_contribution_c|word),
phi ~ 1),
data = filter(df, category == 'abstract'),
family = Beta,
# MCMC settings:
init = 0,
seed = 42,
cores = 4,
iter = 7500,
warmup = 3500,
save_pars = save_pars(all = TRUE), # for bayes factors
control = list(adapt_delta = 0.99))
# Save model:
save(dist_subset_other_mdl,
file = '../models_E2/dist_subset_other_mdl.Rdata')Corresponding null model:
dist_subset_other_null <- brm(bf(closeness_01 ~
# Fixed effects:
1 +
subcluster +
other_contribution_c +
difficulty_c +
# Random effects:
(1 +
subcluster +
other_contribution_c +
subcluster:other_contribution_c|participant) +
(1 + other_contribution_c|word),
phi ~ 1),
data = filter(df, category == 'abstract'),
family = Beta,
# MCMC settings:
init = 0,
seed = 42,
cores = 4,
iter = 7500,
warmup = 3500,
save_pars = save_pars(all = TRUE), # for bayes factors
control = list(adapt_delta = 0.99))
# Save model:
save(dist_subset_other_null,
file = '../models_E2/dist_subset_other_null.Rdata')Load model:
load('../models_E2/dist_subset_other_mdl.Rdata')
load('../models_E2/dist_subset_other_null.Rdata')Show priors:
prior_summary(dist_subset_other_mdl)## prior class coef group
## (flat) b
## (flat) b difficulty_c
## (flat) b other_contribution_c
## (flat) b subclusterEM
## (flat) b subclusterEM:other_contribution_c
## (flat) b subclusterPS
## (flat) b subclusterPS:other_contribution_c
## (flat) b subclusterSS
## (flat) b subclusterSS:other_contribution_c
## student_t(3, 0, 2.5) Intercept
## student_t(3, 0, 2.5) Intercept
## lkj_corr_cholesky(1) L
## lkj_corr_cholesky(1) L participant
## lkj_corr_cholesky(1) L word
## student_t(3, 0, 2.5) sd
## student_t(3, 0, 2.5) sd participant
## student_t(3, 0, 2.5) sd Intercept participant
## student_t(3, 0, 2.5) sd other_contribution_c participant
## student_t(3, 0, 2.5) sd subclusterEM participant
## student_t(3, 0, 2.5) sd subclusterEM:other_contribution_c participant
## student_t(3, 0, 2.5) sd subclusterPS participant
## student_t(3, 0, 2.5) sd subclusterPS:other_contribution_c participant
## student_t(3, 0, 2.5) sd subclusterSS participant
## student_t(3, 0, 2.5) sd subclusterSS:other_contribution_c participant
## student_t(3, 0, 2.5) sd word
## student_t(3, 0, 2.5) sd Intercept word
## student_t(3, 0, 2.5) sd other_contribution_c word
## resp dpar nlpar lb ub source
## default
## (vectorized)
## (vectorized)
## (vectorized)
## (vectorized)
## (vectorized)
## (vectorized)
## (vectorized)
## (vectorized)
## default
## phi default
## default
## (vectorized)
## (vectorized)
## 0 default
## 0 (vectorized)
## 0 (vectorized)
## 0 (vectorized)
## 0 (vectorized)
## 0 (vectorized)
## 0 (vectorized)
## 0 (vectorized)
## 0 (vectorized)
## 0 (vectorized)
## 0 (vectorized)
## 0 (vectorized)
## 0 (vectorized)prior_summary(dist_subset_other_null)## prior class coef group
## (flat) b
## (flat) b difficulty_c
## (flat) b other_contribution_c
## (flat) b subclusterEM
## (flat) b subclusterPS
## (flat) b subclusterSS
## student_t(3, 0, 2.5) Intercept
## student_t(3, 0, 2.5) Intercept
## lkj_corr_cholesky(1) L
## lkj_corr_cholesky(1) L participant
## lkj_corr_cholesky(1) L word
## student_t(3, 0, 2.5) sd
## student_t(3, 0, 2.5) sd participant
## student_t(3, 0, 2.5) sd Intercept participant
## student_t(3, 0, 2.5) sd other_contribution_c participant
## student_t(3, 0, 2.5) sd subclusterEM participant
## student_t(3, 0, 2.5) sd subclusterEM:other_contribution_c participant
## student_t(3, 0, 2.5) sd subclusterPS participant
## student_t(3, 0, 2.5) sd subclusterPS:other_contribution_c participant
## student_t(3, 0, 2.5) sd subclusterSS participant
## student_t(3, 0, 2.5) sd subclusterSS:other_contribution_c participant
## student_t(3, 0, 2.5) sd word
## student_t(3, 0, 2.5) sd Intercept word
## student_t(3, 0, 2.5) sd other_contribution_c word
## resp dpar nlpar lb ub source
## default
## (vectorized)
## (vectorized)
## (vectorized)
## (vectorized)
## (vectorized)
## default
## phi default
## default
## (vectorized)
## (vectorized)
## 0 default
## 0 (vectorized)
## 0 (vectorized)
## 0 (vectorized)
## 0 (vectorized)
## 0 (vectorized)
## 0 (vectorized)
## 0 (vectorized)
## 0 (vectorized)
## 0 (vectorized)
## 0 (vectorized)
## 0 (vectorized)
## 0 (vectorized)Compute Bayes factor:
# Compute bayes factor:
dist_subset_bf <- bayes_factor(dist_subset_other_mdl, dist_subset_other_null)
# Save:
save(dist_subset_bf,
file = '../models_E2/dist_subset_bf.RData')Show Bayes factor:
# # Load:
#
# load('../models_E2/IOS_subset_bf.RData')
#
# # Show:
#
# dist_subset_bfHaving some implementational issues here. Need to check the following warning message:
<<< Error in dyn.load(libLFile) : unable to load shared object ‘/var/folders/mn/d8pyxq412154r5dt7qg7s7rm0000gn/T//RtmpqOZ9uZ/file10301753938d.so’: dlopen(/var/folders/mn/d8pyxq412154r5dt7qg7s7rm0000gn/T//RtmpqOZ9uZ/file10301753938d.so, 6): Library not loaded: /Library/Frameworks/R.framework/Versions/4.2/Resources/lib/libR.dylib Referenced from: /private/var/folders/mn/d8pyxq412154r5dt7qg7s7rm0000gn/T/RtmpqOZ9uZ/file10301753938d.so Reason: Incompatible library version: file10301753938d.so requires version 4.2.0 or later, but libR.dylib provides version 4.1.0 <<<
Check posterior predictive checks of the mixed beta regression:
pp_check(dist_subset_other_mdl, ndraws = 100)
Check this model:
dist_subset_other_mdl## Family: beta
## Links: mu = logit; phi = log
## Formula: closeness_01 ~ 1 + subcluster + other_contribution_c + difficulty_c + subcluster:other_contribution_c + (1 + subcluster + other_contribution_c + subcluster:other_contribution_c | participant) + (1 + other_contribution_c | word)
## phi ~ 1
## Data: filter(df, category == "abstract") (Number of observations: 516)
## Draws: 4 chains, each with iter = 7500; warmup = 3500; thin = 1;
## total post-warmup draws = 16000
##
## Group-Level Effects:
## ~participant (Number of levels: 129)
## Estimate
## sd(Intercept) 0.85
## sd(subclusterEM) 0.13
## sd(subclusterPS) 0.31
## sd(subclusterSS) 0.13
## sd(other_contribution_c) 0.03
## sd(subclusterEM:other_contribution_c) 0.02
## sd(subclusterPS:other_contribution_c) 0.02
## sd(subclusterSS:other_contribution_c) 0.02
## cor(Intercept,subclusterEM) -0.00
## cor(Intercept,subclusterPS) 0.14
## cor(subclusterEM,subclusterPS) -0.01
## cor(Intercept,subclusterSS) 0.03
## cor(subclusterEM,subclusterSS) 0.05
## cor(subclusterPS,subclusterSS) 0.23
## cor(Intercept,other_contribution_c) -0.09
## cor(subclusterEM,other_contribution_c) 0.09
## cor(subclusterPS,other_contribution_c) -0.28
## cor(subclusterSS,other_contribution_c) -0.10
## cor(Intercept,subclusterEM:other_contribution_c) 0.11
## cor(subclusterEM,subclusterEM:other_contribution_c) 0.12
## cor(subclusterPS,subclusterEM:other_contribution_c) -0.08
## cor(subclusterSS,subclusterEM:other_contribution_c) -0.09
## cor(other_contribution_c,subclusterEM:other_contribution_c) -0.24
## cor(Intercept,subclusterPS:other_contribution_c) 0.30
## cor(subclusterEM,subclusterPS:other_contribution_c) -0.05
## cor(subclusterPS,subclusterPS:other_contribution_c) 0.35
## cor(subclusterSS,subclusterPS:other_contribution_c) 0.21
## cor(other_contribution_c,subclusterPS:other_contribution_c) -0.35
## cor(subclusterEM:other_contribution_c,subclusterPS:other_contribution_c) 0.10
## cor(Intercept,subclusterSS:other_contribution_c) -0.14
## cor(subclusterEM,subclusterSS:other_contribution_c) -0.03
## cor(subclusterPS,subclusterSS:other_contribution_c) 0.11
## cor(subclusterSS,subclusterSS:other_contribution_c) 0.18
## cor(other_contribution_c,subclusterSS:other_contribution_c) -0.07
## cor(subclusterEM:other_contribution_c,subclusterSS:other_contribution_c) 0.38
## cor(subclusterPS:other_contribution_c,subclusterSS:other_contribution_c) 0.30
## Est.Error
## sd(Intercept) 0.07
## sd(subclusterEM) 0.09
## sd(subclusterPS) 0.11
## sd(subclusterSS) 0.09
## sd(other_contribution_c) 0.00
## sd(subclusterEM:other_contribution_c) 0.00
## sd(subclusterPS:other_contribution_c) 0.01
## sd(subclusterSS:other_contribution_c) 0.01
## cor(Intercept,subclusterEM) 0.28
## cor(Intercept,subclusterPS) 0.21
## cor(subclusterEM,subclusterPS) 0.32
## cor(Intercept,subclusterSS) 0.29
## cor(subclusterEM,subclusterSS) 0.33
## cor(subclusterPS,subclusterSS) 0.33
## cor(Intercept,other_contribution_c) 0.13
## cor(subclusterEM,other_contribution_c) 0.29
## cor(subclusterPS,other_contribution_c) 0.22
## cor(subclusterSS,other_contribution_c) 0.29
## cor(Intercept,subclusterEM:other_contribution_c) 0.18
## cor(subclusterEM,subclusterEM:other_contribution_c) 0.31
## cor(subclusterPS,subclusterEM:other_contribution_c) 0.25
## cor(subclusterSS,subclusterEM:other_contribution_c) 0.31
## cor(other_contribution_c,subclusterEM:other_contribution_c) 0.21
## cor(Intercept,subclusterPS:other_contribution_c) 0.19
## cor(subclusterEM,subclusterPS:other_contribution_c) 0.32
## cor(subclusterPS,subclusterPS:other_contribution_c) 0.22
## cor(subclusterSS,subclusterPS:other_contribution_c) 0.33
## cor(other_contribution_c,subclusterPS:other_contribution_c) 0.20
## cor(subclusterEM:other_contribution_c,subclusterPS:other_contribution_c) 0.23
## cor(Intercept,subclusterSS:other_contribution_c) 0.23
## cor(subclusterEM,subclusterSS:other_contribution_c) 0.32
## cor(subclusterPS,subclusterSS:other_contribution_c) 0.30
## cor(subclusterSS,subclusterSS:other_contribution_c) 0.32
## cor(other_contribution_c,subclusterSS:other_contribution_c) 0.26
## cor(subclusterEM:other_contribution_c,subclusterSS:other_contribution_c) 0.26
## cor(subclusterPS:other_contribution_c,subclusterSS:other_contribution_c) 0.28
## l-95% CI
## sd(Intercept) 0.72
## sd(subclusterEM) 0.00
## sd(subclusterPS) 0.07
## sd(subclusterSS) 0.01
## sd(other_contribution_c) 0.02
## sd(subclusterEM:other_contribution_c) 0.01
## sd(subclusterPS:other_contribution_c) 0.01
## sd(subclusterSS:other_contribution_c) 0.00
## cor(Intercept,subclusterEM) -0.55
## cor(Intercept,subclusterPS) -0.25
## cor(subclusterEM,subclusterPS) -0.63
## cor(Intercept,subclusterSS) -0.55
## cor(subclusterEM,subclusterSS) -0.59
## cor(subclusterPS,subclusterSS) -0.49
## cor(Intercept,other_contribution_c) -0.35
## cor(subclusterEM,other_contribution_c) -0.50
## cor(subclusterPS,other_contribution_c) -0.68
## cor(subclusterSS,other_contribution_c) -0.62
## cor(Intercept,subclusterEM:other_contribution_c) -0.26
## cor(subclusterEM,subclusterEM:other_contribution_c) -0.51
## cor(subclusterPS,subclusterEM:other_contribution_c) -0.56
## cor(subclusterSS,subclusterEM:other_contribution_c) -0.66
## cor(other_contribution_c,subclusterEM:other_contribution_c) -0.59
## cor(Intercept,subclusterPS:other_contribution_c) -0.08
## cor(subclusterEM,subclusterPS:other_contribution_c) -0.64
## cor(subclusterPS,subclusterPS:other_contribution_c) -0.12
## cor(subclusterSS,subclusterPS:other_contribution_c) -0.48
## cor(other_contribution_c,subclusterPS:other_contribution_c) -0.70
## cor(subclusterEM:other_contribution_c,subclusterPS:other_contribution_c) -0.40
## cor(Intercept,subclusterSS:other_contribution_c) -0.56
## cor(subclusterEM,subclusterSS:other_contribution_c) -0.62
## cor(subclusterPS,subclusterSS:other_contribution_c) -0.51
## cor(subclusterSS,subclusterSS:other_contribution_c) -0.49
## cor(other_contribution_c,subclusterSS:other_contribution_c) -0.55
## cor(subclusterEM:other_contribution_c,subclusterSS:other_contribution_c) -0.29
## cor(subclusterPS:other_contribution_c,subclusterSS:other_contribution_c) -0.34
## u-95% CI
## sd(Intercept) 1.01
## sd(subclusterEM) 0.33
## sd(subclusterPS) 0.54
## sd(subclusterSS) 0.32
## sd(other_contribution_c) 0.04
## sd(subclusterEM:other_contribution_c) 0.03
## sd(subclusterPS:other_contribution_c) 0.04
## sd(subclusterSS:other_contribution_c) 0.03
## cor(Intercept,subclusterEM) 0.56
## cor(Intercept,subclusterPS) 0.57
## cor(subclusterEM,subclusterPS) 0.59
## cor(Intercept,subclusterSS) 0.58
## cor(subclusterEM,subclusterSS) 0.66
## cor(subclusterPS,subclusterSS) 0.77
## cor(Intercept,other_contribution_c) 0.17
## cor(subclusterEM,other_contribution_c) 0.62
## cor(subclusterPS,other_contribution_c) 0.19
## cor(subclusterSS,other_contribution_c) 0.51
## cor(Intercept,subclusterEM:other_contribution_c) 0.46
## cor(subclusterEM,subclusterEM:other_contribution_c) 0.67
## cor(subclusterPS,subclusterEM:other_contribution_c) 0.43
## cor(subclusterSS,subclusterEM:other_contribution_c) 0.54
## cor(other_contribution_c,subclusterEM:other_contribution_c) 0.21
## cor(Intercept,subclusterPS:other_contribution_c) 0.66
## cor(subclusterEM,subclusterPS:other_contribution_c) 0.60
## cor(subclusterPS,subclusterPS:other_contribution_c) 0.75
## cor(subclusterSS,subclusterPS:other_contribution_c) 0.76
## cor(other_contribution_c,subclusterPS:other_contribution_c) 0.08
## cor(subclusterEM:other_contribution_c,subclusterPS:other_contribution_c) 0.52
## cor(Intercept,subclusterSS:other_contribution_c) 0.34
## cor(subclusterEM,subclusterSS:other_contribution_c) 0.59
## cor(subclusterPS,subclusterSS:other_contribution_c) 0.65
## cor(subclusterSS,subclusterSS:other_contribution_c) 0.72
## cor(other_contribution_c,subclusterSS:other_contribution_c) 0.46
## cor(subclusterEM:other_contribution_c,subclusterSS:other_contribution_c) 0.76
## cor(subclusterPS:other_contribution_c,subclusterSS:other_contribution_c) 0.75
## Rhat
## sd(Intercept) 1.00
## sd(subclusterEM) 1.00
## sd(subclusterPS) 1.00
## sd(subclusterSS) 1.00
## sd(other_contribution_c) 1.00
## sd(subclusterEM:other_contribution_c) 1.00
## sd(subclusterPS:other_contribution_c) 1.00
## sd(subclusterSS:other_contribution_c) 1.00
## cor(Intercept,subclusterEM) 1.00
## cor(Intercept,subclusterPS) 1.00
## cor(subclusterEM,subclusterPS) 1.00
## cor(Intercept,subclusterSS) 1.00
## cor(subclusterEM,subclusterSS) 1.00
## cor(subclusterPS,subclusterSS) 1.00
## cor(Intercept,other_contribution_c) 1.00
## cor(subclusterEM,other_contribution_c) 1.00
## cor(subclusterPS,other_contribution_c) 1.00
## cor(subclusterSS,other_contribution_c) 1.00
## cor(Intercept,subclusterEM:other_contribution_c) 1.00
## cor(subclusterEM,subclusterEM:other_contribution_c) 1.00
## cor(subclusterPS,subclusterEM:other_contribution_c) 1.00
## cor(subclusterSS,subclusterEM:other_contribution_c) 1.00
## cor(other_contribution_c,subclusterEM:other_contribution_c) 1.00
## cor(Intercept,subclusterPS:other_contribution_c) 1.00
## cor(subclusterEM,subclusterPS:other_contribution_c) 1.00
## cor(subclusterPS,subclusterPS:other_contribution_c) 1.00
## cor(subclusterSS,subclusterPS:other_contribution_c) 1.00
## cor(other_contribution_c,subclusterPS:other_contribution_c) 1.00
## cor(subclusterEM:other_contribution_c,subclusterPS:other_contribution_c) 1.00
## cor(Intercept,subclusterSS:other_contribution_c) 1.00
## cor(subclusterEM,subclusterSS:other_contribution_c) 1.00
## cor(subclusterPS,subclusterSS:other_contribution_c) 1.00
## cor(subclusterSS,subclusterSS:other_contribution_c) 1.00
## cor(other_contribution_c,subclusterSS:other_contribution_c) 1.00
## cor(subclusterEM:other_contribution_c,subclusterSS:other_contribution_c) 1.00
## cor(subclusterPS:other_contribution_c,subclusterSS:other_contribution_c) 1.00
## Bulk_ESS
## sd(Intercept) 3262
## sd(subclusterEM) 1138
## sd(subclusterPS) 855
## sd(subclusterSS) 1532
## sd(other_contribution_c) 3296
## sd(subclusterEM:other_contribution_c) 1093
## sd(subclusterPS:other_contribution_c) 1271
## sd(subclusterSS:other_contribution_c) 881
## cor(Intercept,subclusterEM) 10047
## cor(Intercept,subclusterPS) 3996
## cor(subclusterEM,subclusterPS) 1545
## cor(Intercept,subclusterSS) 13487
## cor(subclusterEM,subclusterSS) 4040
## cor(subclusterPS,subclusterSS) 3306
## cor(Intercept,other_contribution_c) 4326
## cor(subclusterEM,other_contribution_c) 822
## cor(subclusterPS,other_contribution_c) 1480
## cor(subclusterSS,other_contribution_c) 1047
## cor(Intercept,subclusterEM:other_contribution_c) 5320
## cor(subclusterEM,subclusterEM:other_contribution_c) 1297
## cor(subclusterPS,subclusterEM:other_contribution_c) 2105
## cor(subclusterSS,subclusterEM:other_contribution_c) 1772
## cor(other_contribution_c,subclusterEM:other_contribution_c) 3196
## cor(Intercept,subclusterPS:other_contribution_c) 2980
## cor(subclusterEM,subclusterPS:other_contribution_c) 1421
## cor(subclusterPS,subclusterPS:other_contribution_c) 2473
## cor(subclusterSS,subclusterPS:other_contribution_c) 1890
## cor(other_contribution_c,subclusterPS:other_contribution_c) 4128
## cor(subclusterEM:other_contribution_c,subclusterPS:other_contribution_c) 2160
## cor(Intercept,subclusterSS:other_contribution_c) 6215
## cor(subclusterEM,subclusterSS:other_contribution_c) 2292
## cor(subclusterPS,subclusterSS:other_contribution_c) 3005
## cor(subclusterSS,subclusterSS:other_contribution_c) 2448
## cor(other_contribution_c,subclusterSS:other_contribution_c) 4544
## cor(subclusterEM:other_contribution_c,subclusterSS:other_contribution_c) 1858
## cor(subclusterPS:other_contribution_c,subclusterSS:other_contribution_c) 3450
## Tail_ESS
## sd(Intercept) 5453
## sd(subclusterEM) 2348
## sd(subclusterPS) 1619
## sd(subclusterSS) 3651
## sd(other_contribution_c) 6559
## sd(subclusterEM:other_contribution_c) 1987
## sd(subclusterPS:other_contribution_c) 2708
## sd(subclusterSS:other_contribution_c) 1629
## cor(Intercept,subclusterEM) 9596
## cor(Intercept,subclusterPS) 6121
## cor(subclusterEM,subclusterPS) 4027
## cor(Intercept,subclusterSS) 10556
## cor(subclusterEM,subclusterSS) 8287
## cor(subclusterPS,subclusterSS) 8845
## cor(Intercept,other_contribution_c) 8196
## cor(subclusterEM,other_contribution_c) 1553
## cor(subclusterPS,other_contribution_c) 2415
## cor(subclusterSS,other_contribution_c) 2343
## cor(Intercept,subclusterEM:other_contribution_c) 6938
## cor(subclusterEM,subclusterEM:other_contribution_c) 2733
## cor(subclusterPS,subclusterEM:other_contribution_c) 4326
## cor(subclusterSS,subclusterEM:other_contribution_c) 3863
## cor(other_contribution_c,subclusterEM:other_contribution_c) 4580
## cor(Intercept,subclusterPS:other_contribution_c) 5683
## cor(subclusterEM,subclusterPS:other_contribution_c) 3467
## cor(subclusterPS,subclusterPS:other_contribution_c) 4162
## cor(subclusterSS,subclusterPS:other_contribution_c) 4533
## cor(other_contribution_c,subclusterPS:other_contribution_c) 7002
## cor(subclusterEM:other_contribution_c,subclusterPS:other_contribution_c) 3628
## cor(Intercept,subclusterSS:other_contribution_c) 7479
## cor(subclusterEM,subclusterSS:other_contribution_c) 5399
## cor(subclusterPS,subclusterSS:other_contribution_c) 6433
## cor(subclusterSS,subclusterSS:other_contribution_c) 4589
## cor(other_contribution_c,subclusterSS:other_contribution_c) 8540
## cor(subclusterEM:other_contribution_c,subclusterSS:other_contribution_c) 3287
## cor(subclusterPS:other_contribution_c,subclusterSS:other_contribution_c) 5888
##
## ~word (Number of levels: 16)
## Estimate Est.Error l-95% CI u-95% CI Rhat
## sd(Intercept) 0.06 0.04 0.00 0.16 1.00
## sd(other_contribution_c) 0.00 0.00 0.00 0.01 1.00
## cor(Intercept,other_contribution_c) 0.13 0.56 -0.91 0.97 1.00
## Bulk_ESS Tail_ESS
## sd(Intercept) 3007 5319
## sd(other_contribution_c) 4453 6921
## cor(Intercept,other_contribution_c) 6801 9617
##
## Population-Level Effects:
## Estimate Est.Error l-95% CI u-95% CI Rhat
## Intercept 0.98 0.10 0.79 1.16 1.00
## phi_Intercept 4.13 0.20 3.76 4.51 1.00
## subclusterEM -0.04 0.07 -0.18 0.10 1.00
## subclusterPS 0.01 0.08 -0.15 0.17 1.00
## subclusterSS -0.08 0.08 -0.24 0.08 1.00
## other_contribution_c 0.02 0.00 0.01 0.02 1.00
## difficulty_c -0.00 0.00 -0.01 -0.00 1.00
## subclusterEM:other_contribution_c -0.00 0.00 -0.01 0.01 1.00
## subclusterPS:other_contribution_c -0.00 0.00 -0.01 0.01 1.00
## subclusterSS:other_contribution_c -0.00 0.00 -0.01 0.01 1.00
## Bulk_ESS Tail_ESS
## Intercept 2168 4480
## phi_Intercept 646 2162
## subclusterEM 6863 6781
## subclusterPS 6887 7389
## subclusterSS 7373 7261
## other_contribution_c 6324 8474
## difficulty_c 7416 11110
## subclusterEM:other_contribution_c 5462 6721
## subclusterPS:other_contribution_c 7214 8040
## subclusterSS:other_contribution_c 6674 7911
##
## Draws were sampled using sampling(NUTS). For each parameter, Bulk_ESS
## and Tail_ESS are effective sample size measures, and Rhat is the potential
## scale reduction factor on split chains (at convergence, Rhat = 1).Perform hypothesis tests on the fixed effects coefficient:
hypothesis(dist_subset_other_mdl,
'difficulty_c < 0')## Hypothesis Tests for class b:
## Hypothesis Estimate Est.Error CI.Lower CI.Upper Evid.Ratio Post.Prob
## 1 (difficulty_c) < 0 0 0 -0.01 0 1599 1
## Star
## 1 *
## ---
## 'CI': 90%-CI for one-sided and 95%-CI for two-sided hypotheses.
## '*': For one-sided hypotheses, the posterior probability exceeds 95%;
## for two-sided hypotheses, the value tested against lies outside the 95%-CI.
## Posterior probabilities of point hypotheses assume equal prior probabilities.hypothesis(dist_subset_other_mdl,
'other_contribution_c > 0')## Hypothesis Tests for class b:
## Hypothesis Estimate Est.Error CI.Lower CI.Upper Evid.Ratio
## 1 (other_contributi... > 0 0.02 0 0.01 0.02 1229.77
## Post.Prob Star
## 1 1 *
## ---
## 'CI': 90%-CI for one-sided and 95%-CI for two-sided hypotheses.
## '*': For one-sided hypotheses, the posterior probability exceeds 95%;
## for two-sided hypotheses, the value tested against lies outside the 95%-CI.
## Posterior probabilities of point hypotheses assume equal prior probabilities.hypothesis(dist_subset_other_mdl,
'subclusterEM:other_contribution_c < 0') # PSTQ is reference## Hypothesis Tests for class b:
## Hypothesis Estimate Est.Error CI.Lower CI.Upper Evid.Ratio
## 1 (subclusterEM:oth... < 0 0 0 -0.01 0.01 1.8
## Post.Prob Star
## 1 0.64
## ---
## 'CI': 90%-CI for one-sided and 95%-CI for two-sided hypotheses.
## '*': For one-sided hypotheses, the posterior probability exceeds 95%;
## for two-sided hypotheses, the value tested against lies outside the 95%-CI.
## Posterior probabilities of point hypotheses assume equal prior probabilities.hypothesis(dist_subset_other_mdl,
'subclusterPS:other_contribution_c < 0') # PSTQ is reference## Hypothesis Tests for class b:
## Hypothesis Estimate Est.Error CI.Lower CI.Upper Evid.Ratio
## 1 (subclusterPS:oth... < 0 0 0 -0.01 0.01 2.43
## Post.Prob Star
## 1 0.71
## ---
## 'CI': 90%-CI for one-sided and 95%-CI for two-sided hypotheses.
## '*': For one-sided hypotheses, the posterior probability exceeds 95%;
## for two-sided hypotheses, the value tested against lies outside the 95%-CI.
## Posterior probabilities of point hypotheses assume equal prior probabilities.hypothesis(dist_subset_other_mdl,
'subclusterSS:other_contribution_c < 0') # PSTQ is reference## Hypothesis Tests for class b:
## Hypothesis Estimate Est.Error CI.Lower CI.Upper Evid.Ratio
## 1 (subclusterSS:oth... < 0 0 0 -0.01 0.01 2.18
## Post.Prob Star
## 1 0.69
## ---
## 'CI': 90%-CI for one-sided and 95%-CI for two-sided hypotheses.
## '*': For one-sided hypotheses, the posterior probability exceeds 95%;
## for two-sided hypotheses, the value tested against lies outside the 95%-CI.
## Posterior probabilities of point hypotheses assume equal prior probabilities.Finally, the distance model with self contribution as covariate, again for only the abstract concepts.
dist_subset_self_mdl <- brm(bf(closeness_01 ~
# Fixed effects:
1 +
subcluster +
self_contribution_c +
difficulty_c +
subcluster:self_contribution_c +
# Random effects:
(1 +
subcluster +
self_contribution_c +
subcluster:self_contribution_c|participant) +
(1 + self_contribution_c|word),
phi ~ 1),
data = filter(df, category == 'abstract'),
family = Beta,
# MCMC settings:
init = 0,
seed = 42,
cores = 4,
iter = 7500,
warmup = 3500, # higher because ESS low warning
save_pars = save_pars(all = TRUE), # for bayes factors
control = list(adapt_delta = 0.99))
# Save model:
save(dist_subset_self_mdl,
file = '../models_E2/dist_subset_self_mdl.Rdata')The corresponding null model:
dist_subset_self_null <- brm(bf(closeness_01 ~
# Fixed effects:
1 +
subcluster +
self_contribution_c +
difficulty_c +
# Random effects:
(1 +
subcluster +
self_contribution_c +
subcluster:self_contribution_c|participant) +
(1 + self_contribution_c|word),
phi ~ 1),
data = filter(df, category == 'abstract'),
family = Beta,
# MCMC settings:
init = 0,
seed = 42,
cores = 4,
iter = 7500,
warmup = 3500, # higher because ESS low warning
save_pars = save_pars(all = TRUE), # for bayes factors
control = list(adapt_delta = 0.99))
# Save model:
save(dist_subset_self_null,
file = '../models_E2/dist_subset_self_null.Rdata')Load model:
load('../models_E2/dist_subset_self_mdl.Rdata')
load('../models_E2/dist_subset_self_null.Rdata')Show priors:
prior_summary(dist_subset_self_mdl)## prior class coef group
## (flat) b
## (flat) b difficulty_c
## (flat) b self_contribution_c
## (flat) b subclusterEM
## (flat) b subclusterEM:self_contribution_c
## (flat) b subclusterPS
## (flat) b subclusterPS:self_contribution_c
## (flat) b subclusterSS
## (flat) b subclusterSS:self_contribution_c
## student_t(3, 0, 2.5) Intercept
## student_t(3, 0, 2.5) Intercept
## lkj_corr_cholesky(1) L
## lkj_corr_cholesky(1) L participant
## lkj_corr_cholesky(1) L word
## student_t(3, 0, 2.5) sd
## student_t(3, 0, 2.5) sd participant
## student_t(3, 0, 2.5) sd Intercept participant
## student_t(3, 0, 2.5) sd self_contribution_c participant
## student_t(3, 0, 2.5) sd subclusterEM participant
## student_t(3, 0, 2.5) sd subclusterEM:self_contribution_c participant
## student_t(3, 0, 2.5) sd subclusterPS participant
## student_t(3, 0, 2.5) sd subclusterPS:self_contribution_c participant
## student_t(3, 0, 2.5) sd subclusterSS participant
## student_t(3, 0, 2.5) sd subclusterSS:self_contribution_c participant
## student_t(3, 0, 2.5) sd word
## student_t(3, 0, 2.5) sd Intercept word
## student_t(3, 0, 2.5) sd self_contribution_c word
## resp dpar nlpar lb ub source
## default
## (vectorized)
## (vectorized)
## (vectorized)
## (vectorized)
## (vectorized)
## (vectorized)
## (vectorized)
## (vectorized)
## default
## phi default
## default
## (vectorized)
## (vectorized)
## 0 default
## 0 (vectorized)
## 0 (vectorized)
## 0 (vectorized)
## 0 (vectorized)
## 0 (vectorized)
## 0 (vectorized)
## 0 (vectorized)
## 0 (vectorized)
## 0 (vectorized)
## 0 (vectorized)
## 0 (vectorized)
## 0 (vectorized)prior_summary(dist_subset_self_null)## prior class coef group
## (flat) b
## (flat) b difficulty_c
## (flat) b self_contribution_c
## (flat) b subclusterEM
## (flat) b subclusterPS
## (flat) b subclusterSS
## student_t(3, 0, 2.5) Intercept
## student_t(3, 0, 2.5) Intercept
## lkj_corr_cholesky(1) L
## lkj_corr_cholesky(1) L participant
## lkj_corr_cholesky(1) L word
## student_t(3, 0, 2.5) sd
## student_t(3, 0, 2.5) sd participant
## student_t(3, 0, 2.5) sd Intercept participant
## student_t(3, 0, 2.5) sd self_contribution_c participant
## student_t(3, 0, 2.5) sd subclusterEM participant
## student_t(3, 0, 2.5) sd subclusterEM:self_contribution_c participant
## student_t(3, 0, 2.5) sd subclusterPS participant
## student_t(3, 0, 2.5) sd subclusterPS:self_contribution_c participant
## student_t(3, 0, 2.5) sd subclusterSS participant
## student_t(3, 0, 2.5) sd subclusterSS:self_contribution_c participant
## student_t(3, 0, 2.5) sd word
## student_t(3, 0, 2.5) sd Intercept word
## student_t(3, 0, 2.5) sd self_contribution_c word
## resp dpar nlpar lb ub source
## default
## (vectorized)
## (vectorized)
## (vectorized)
## (vectorized)
## (vectorized)
## default
## phi default
## default
## (vectorized)
## (vectorized)
## 0 default
## 0 (vectorized)
## 0 (vectorized)
## 0 (vectorized)
## 0 (vectorized)
## 0 (vectorized)
## 0 (vectorized)
## 0 (vectorized)
## 0 (vectorized)
## 0 (vectorized)
## 0 (vectorized)
## 0 (vectorized)
## 0 (vectorized)Compute Bayes factor:
# Compute bayes factor:
dist_subset_self_bf <- bayes_factor(dist_subset_self_mdl.Rdata,
dist_subset_self_null)
# Save:
save(dist_self_bf,
file = '../models_E2/dist_subset_self_bf.RData')Same as above with the error…
Show Bayes factor:
# # Load:
#
# load('../models_E2/dist_subset_self_bf.RData')
#
# # Show:
#
# dist_subset_self_bfCheck posterior predictive checks of the mixed beta regression:
pp_check(dist_subset_self_mdl, ndraws = 100)
Check this model:
dist_subset_self_mdl## Family: beta
## Links: mu = logit; phi = log
## Formula: closeness_01 ~ 1 + subcluster + self_contribution_c + difficulty_c + subcluster:self_contribution_c + (1 + subcluster + self_contribution_c + subcluster:self_contribution_c | participant) + (1 + self_contribution_c | word)
## phi ~ 1
## Data: filter(df, category == "abstract") (Number of observations: 516)
## Draws: 4 chains, each with iter = 7500; warmup = 3500; thin = 1;
## total post-warmup draws = 16000
##
## Group-Level Effects:
## ~participant (Number of levels: 129)
## Estimate
## sd(Intercept) 0.87
## sd(subclusterEM) 0.50
## sd(subclusterPS) 0.71
## sd(subclusterSS) 0.33
## sd(self_contribution_c) 0.03
## sd(subclusterEM:self_contribution_c) 0.01
## sd(subclusterPS:self_contribution_c) 0.02
## sd(subclusterSS:self_contribution_c) 0.01
## cor(Intercept,subclusterEM) -0.26
## cor(Intercept,subclusterPS) -0.13
## cor(subclusterEM,subclusterPS) 0.34
## cor(Intercept,subclusterSS) -0.15
## cor(subclusterEM,subclusterSS) 0.53
## cor(subclusterPS,subclusterSS) 0.54
## cor(Intercept,self_contribution_c) -0.04
## cor(subclusterEM,self_contribution_c) 0.28
## cor(subclusterPS,self_contribution_c) 0.18
## cor(subclusterSS,self_contribution_c) 0.52
## cor(Intercept,subclusterEM:self_contribution_c) -0.05
## cor(subclusterEM,subclusterEM:self_contribution_c) 0.44
## cor(subclusterPS,subclusterEM:self_contribution_c) 0.01
## cor(subclusterSS,subclusterEM:self_contribution_c) 0.15
## cor(self_contribution_c,subclusterEM:self_contribution_c) -0.07
## cor(Intercept,subclusterPS:self_contribution_c) 0.26
## cor(subclusterEM,subclusterPS:self_contribution_c) -0.14
## cor(subclusterPS,subclusterPS:self_contribution_c) 0.48
## cor(subclusterSS,subclusterPS:self_contribution_c) 0.10
## cor(self_contribution_c,subclusterPS:self_contribution_c) -0.18
## cor(subclusterEM:self_contribution_c,subclusterPS:self_contribution_c) -0.04
## cor(Intercept,subclusterSS:self_contribution_c) -0.34
## cor(subclusterEM,subclusterSS:self_contribution_c) 0.18
## cor(subclusterPS,subclusterSS:self_contribution_c) 0.19
## cor(subclusterSS,subclusterSS:self_contribution_c) 0.28
## cor(self_contribution_c,subclusterSS:self_contribution_c) 0.18
## cor(subclusterEM:self_contribution_c,subclusterSS:self_contribution_c) 0.16
## cor(subclusterPS:self_contribution_c,subclusterSS:self_contribution_c) 0.02
## Est.Error
## sd(Intercept) 0.07
## sd(subclusterEM) 0.07
## sd(subclusterPS) 0.08
## sd(subclusterSS) 0.08
## sd(self_contribution_c) 0.00
## sd(subclusterEM:self_contribution_c) 0.00
## sd(subclusterPS:self_contribution_c) 0.01
## sd(subclusterSS:self_contribution_c) 0.00
## cor(Intercept,subclusterEM) 0.12
## cor(Intercept,subclusterPS) 0.13
## cor(subclusterEM,subclusterPS) 0.13
## cor(Intercept,subclusterSS) 0.18
## cor(subclusterEM,subclusterSS) 0.17
## cor(subclusterPS,subclusterSS) 0.18
## cor(Intercept,self_contribution_c) 0.14
## cor(subclusterEM,self_contribution_c) 0.15
## cor(subclusterPS,self_contribution_c) 0.15
## cor(subclusterSS,self_contribution_c) 0.19
## cor(Intercept,subclusterEM:self_contribution_c) 0.27
## cor(subclusterEM,subclusterEM:self_contribution_c) 0.26
## cor(subclusterPS,subclusterEM:self_contribution_c) 0.28
## cor(subclusterSS,subclusterEM:self_contribution_c) 0.29
## cor(self_contribution_c,subclusterEM:self_contribution_c) 0.28
## cor(Intercept,subclusterPS:self_contribution_c) 0.23
## cor(subclusterEM,subclusterPS:self_contribution_c) 0.25
## cor(subclusterPS,subclusterPS:self_contribution_c) 0.21
## cor(subclusterSS,subclusterPS:self_contribution_c) 0.28
## cor(self_contribution_c,subclusterPS:self_contribution_c) 0.25
## cor(subclusterEM:self_contribution_c,subclusterPS:self_contribution_c) 0.30
## cor(Intercept,subclusterSS:self_contribution_c) 0.27
## cor(subclusterEM,subclusterSS:self_contribution_c) 0.28
## cor(subclusterPS,subclusterSS:self_contribution_c) 0.30
## cor(subclusterSS,subclusterSS:self_contribution_c) 0.30
## cor(self_contribution_c,subclusterSS:self_contribution_c) 0.28
## cor(subclusterEM:self_contribution_c,subclusterSS:self_contribution_c) 0.32
## cor(subclusterPS:self_contribution_c,subclusterSS:self_contribution_c) 0.31
## l-95% CI
## sd(Intercept) 0.73
## sd(subclusterEM) 0.36
## sd(subclusterPS) 0.55
## sd(subclusterSS) 0.15
## sd(self_contribution_c) 0.02
## sd(subclusterEM:self_contribution_c) 0.00
## sd(subclusterPS:self_contribution_c) 0.00
## sd(subclusterSS:self_contribution_c) 0.00
## cor(Intercept,subclusterEM) -0.48
## cor(Intercept,subclusterPS) -0.36
## cor(subclusterEM,subclusterPS) 0.06
## cor(Intercept,subclusterSS) -0.47
## cor(subclusterEM,subclusterSS) 0.13
## cor(subclusterPS,subclusterSS) 0.13
## cor(Intercept,self_contribution_c) -0.31
## cor(subclusterEM,self_contribution_c) -0.04
## cor(subclusterPS,self_contribution_c) -0.11
## cor(subclusterSS,self_contribution_c) 0.09
## cor(Intercept,subclusterEM:self_contribution_c) -0.58
## cor(subclusterEM,subclusterEM:self_contribution_c) -0.18
## cor(subclusterPS,subclusterEM:self_contribution_c) -0.52
## cor(subclusterSS,subclusterEM:self_contribution_c) -0.46
## cor(self_contribution_c,subclusterEM:self_contribution_c) -0.59
## cor(Intercept,subclusterPS:self_contribution_c) -0.24
## cor(subclusterEM,subclusterPS:self_contribution_c) -0.59
## cor(subclusterPS,subclusterPS:self_contribution_c) -0.02
## cor(subclusterSS,subclusterPS:self_contribution_c) -0.47
## cor(self_contribution_c,subclusterPS:self_contribution_c) -0.62
## cor(subclusterEM:self_contribution_c,subclusterPS:self_contribution_c) -0.61
## cor(Intercept,subclusterSS:self_contribution_c) -0.78
## cor(subclusterEM,subclusterSS:self_contribution_c) -0.42
## cor(subclusterPS,subclusterSS:self_contribution_c) -0.45
## cor(subclusterSS,subclusterSS:self_contribution_c) -0.39
## cor(self_contribution_c,subclusterSS:self_contribution_c) -0.42
## cor(subclusterEM:self_contribution_c,subclusterSS:self_contribution_c) -0.50
## cor(subclusterPS:self_contribution_c,subclusterSS:self_contribution_c) -0.59
## u-95% CI
## sd(Intercept) 1.01
## sd(subclusterEM) 0.63
## sd(subclusterPS) 0.87
## sd(subclusterSS) 0.48
## sd(self_contribution_c) 0.03
## sd(subclusterEM:self_contribution_c) 0.02
## sd(subclusterPS:self_contribution_c) 0.03
## sd(subclusterSS:self_contribution_c) 0.02
## cor(Intercept,subclusterEM) -0.00
## cor(Intercept,subclusterPS) 0.13
## cor(subclusterEM,subclusterPS) 0.58
## cor(Intercept,subclusterSS) 0.23
## cor(subclusterEM,subclusterSS) 0.80
## cor(subclusterPS,subclusterSS) 0.83
## cor(Intercept,self_contribution_c) 0.25
## cor(subclusterEM,self_contribution_c) 0.57
## cor(subclusterPS,self_contribution_c) 0.45
## cor(subclusterSS,self_contribution_c) 0.83
## cor(Intercept,subclusterEM:self_contribution_c) 0.49
## cor(subclusterEM,subclusterEM:self_contribution_c) 0.83
## cor(subclusterPS,subclusterEM:self_contribution_c) 0.54
## cor(subclusterSS,subclusterEM:self_contribution_c) 0.68
## cor(self_contribution_c,subclusterEM:self_contribution_c) 0.51
## cor(Intercept,subclusterPS:self_contribution_c) 0.65
## cor(subclusterEM,subclusterPS:self_contribution_c) 0.39
## cor(subclusterPS,subclusterPS:self_contribution_c) 0.81
## cor(subclusterSS,subclusterPS:self_contribution_c) 0.63
## cor(self_contribution_c,subclusterPS:self_contribution_c) 0.36
## cor(subclusterEM:self_contribution_c,subclusterPS:self_contribution_c) 0.53
## cor(Intercept,subclusterSS:self_contribution_c) 0.29
## cor(subclusterEM,subclusterSS:self_contribution_c) 0.67
## cor(subclusterPS,subclusterSS:self_contribution_c) 0.71
## cor(subclusterSS,subclusterSS:self_contribution_c) 0.77
## cor(self_contribution_c,subclusterSS:self_contribution_c) 0.68
## cor(subclusterEM:self_contribution_c,subclusterSS:self_contribution_c) 0.71
## cor(subclusterPS:self_contribution_c,subclusterSS:self_contribution_c) 0.60
## Rhat
## sd(Intercept) 1.00
## sd(subclusterEM) 1.00
## sd(subclusterPS) 1.00
## sd(subclusterSS) 1.00
## sd(self_contribution_c) 1.00
## sd(subclusterEM:self_contribution_c) 1.00
## sd(subclusterPS:self_contribution_c) 1.00
## sd(subclusterSS:self_contribution_c) 1.00
## cor(Intercept,subclusterEM) 1.00
## cor(Intercept,subclusterPS) 1.00
## cor(subclusterEM,subclusterPS) 1.00
## cor(Intercept,subclusterSS) 1.00
## cor(subclusterEM,subclusterSS) 1.00
## cor(subclusterPS,subclusterSS) 1.00
## cor(Intercept,self_contribution_c) 1.00
## cor(subclusterEM,self_contribution_c) 1.00
## cor(subclusterPS,self_contribution_c) 1.00
## cor(subclusterSS,self_contribution_c) 1.00
## cor(Intercept,subclusterEM:self_contribution_c) 1.00
## cor(subclusterEM,subclusterEM:self_contribution_c) 1.00
## cor(subclusterPS,subclusterEM:self_contribution_c) 1.00
## cor(subclusterSS,subclusterEM:self_contribution_c) 1.00
## cor(self_contribution_c,subclusterEM:self_contribution_c) 1.00
## cor(Intercept,subclusterPS:self_contribution_c) 1.00
## cor(subclusterEM,subclusterPS:self_contribution_c) 1.00
## cor(subclusterPS,subclusterPS:self_contribution_c) 1.00
## cor(subclusterSS,subclusterPS:self_contribution_c) 1.00
## cor(self_contribution_c,subclusterPS:self_contribution_c) 1.00
## cor(subclusterEM:self_contribution_c,subclusterPS:self_contribution_c) 1.00
## cor(Intercept,subclusterSS:self_contribution_c) 1.00
## cor(subclusterEM,subclusterSS:self_contribution_c) 1.00
## cor(subclusterPS,subclusterSS:self_contribution_c) 1.00
## cor(subclusterSS,subclusterSS:self_contribution_c) 1.00
## cor(self_contribution_c,subclusterSS:self_contribution_c) 1.00
## cor(subclusterEM:self_contribution_c,subclusterSS:self_contribution_c) 1.00
## cor(subclusterPS:self_contribution_c,subclusterSS:self_contribution_c) 1.00
## Bulk_ESS
## sd(Intercept) 3559
## sd(subclusterEM) 1720
## sd(subclusterPS) 1513
## sd(subclusterSS) 1534
## sd(self_contribution_c) 3236
## sd(subclusterEM:self_contribution_c) 2469
## sd(subclusterPS:self_contribution_c) 1747
## sd(subclusterSS:self_contribution_c) 2140
## cor(Intercept,subclusterEM) 5067
## cor(Intercept,subclusterPS) 2865
## cor(subclusterEM,subclusterPS) 2371
## cor(Intercept,subclusterSS) 5771
## cor(subclusterEM,subclusterSS) 4361
## cor(subclusterPS,subclusterSS) 3584
## cor(Intercept,self_contribution_c) 4973
## cor(subclusterEM,self_contribution_c) 4070
## cor(subclusterPS,self_contribution_c) 4849
## cor(subclusterSS,self_contribution_c) 1763
## cor(Intercept,subclusterEM:self_contribution_c) 8604
## cor(subclusterEM,subclusterEM:self_contribution_c) 5657
## cor(subclusterPS,subclusterEM:self_contribution_c) 9411
## cor(subclusterSS,subclusterEM:self_contribution_c) 6820
## cor(self_contribution_c,subclusterEM:self_contribution_c) 9119
## cor(Intercept,subclusterPS:self_contribution_c) 4880
## cor(subclusterEM,subclusterPS:self_contribution_c) 5640
## cor(subclusterPS,subclusterPS:self_contribution_c) 5918
## cor(subclusterSS,subclusterPS:self_contribution_c) 4754
## cor(self_contribution_c,subclusterPS:self_contribution_c) 5162
## cor(subclusterEM:self_contribution_c,subclusterPS:self_contribution_c) 6680
## cor(Intercept,subclusterSS:self_contribution_c) 7812
## cor(subclusterEM,subclusterSS:self_contribution_c) 9184
## cor(subclusterPS,subclusterSS:self_contribution_c) 9095
## cor(subclusterSS,subclusterSS:self_contribution_c) 5466
## cor(self_contribution_c,subclusterSS:self_contribution_c) 11519
## cor(subclusterEM:self_contribution_c,subclusterSS:self_contribution_c) 6897
## cor(subclusterPS:self_contribution_c,subclusterSS:self_contribution_c) 9511
## Tail_ESS
## sd(Intercept) 6898
## sd(subclusterEM) 2520
## sd(subclusterPS) 2731
## sd(subclusterSS) 1817
## sd(self_contribution_c) 5554
## sd(subclusterEM:self_contribution_c) 4103
## sd(subclusterPS:self_contribution_c) 2379
## sd(subclusterSS:self_contribution_c) 5199
## cor(Intercept,subclusterEM) 6795
## cor(Intercept,subclusterPS) 4104
## cor(subclusterEM,subclusterPS) 3825
## cor(Intercept,subclusterSS) 6289
## cor(subclusterEM,subclusterSS) 4691
## cor(subclusterPS,subclusterSS) 4804
## cor(Intercept,self_contribution_c) 8677
## cor(subclusterEM,self_contribution_c) 6765
## cor(subclusterPS,self_contribution_c) 8836
## cor(subclusterSS,self_contribution_c) 1967
## cor(Intercept,subclusterEM:self_contribution_c) 11469
## cor(subclusterEM,subclusterEM:self_contribution_c) 7332
## cor(subclusterPS,subclusterEM:self_contribution_c) 11221
## cor(subclusterSS,subclusterEM:self_contribution_c) 10010
## cor(self_contribution_c,subclusterEM:self_contribution_c) 11852
## cor(Intercept,subclusterPS:self_contribution_c) 6790
## cor(subclusterEM,subclusterPS:self_contribution_c) 8355
## cor(subclusterPS,subclusterPS:self_contribution_c) 6732
## cor(subclusterSS,subclusterPS:self_contribution_c) 8699
## cor(self_contribution_c,subclusterPS:self_contribution_c) 8018
## cor(subclusterEM:self_contribution_c,subclusterPS:self_contribution_c) 11127
## cor(Intercept,subclusterSS:self_contribution_c) 8763
## cor(subclusterEM,subclusterSS:self_contribution_c) 9689
## cor(subclusterPS,subclusterSS:self_contribution_c) 10743
## cor(subclusterSS,subclusterSS:self_contribution_c) 8895
## cor(self_contribution_c,subclusterSS:self_contribution_c) 10366
## cor(subclusterEM:self_contribution_c,subclusterSS:self_contribution_c) 11853
## cor(subclusterPS:self_contribution_c,subclusterSS:self_contribution_c) 12206
##
## ~word (Number of levels: 16)
## Estimate Est.Error l-95% CI u-95% CI Rhat
## sd(Intercept) 0.06 0.04 0.00 0.17 1.00
## sd(self_contribution_c) 0.00 0.00 0.00 0.01 1.00
## cor(Intercept,self_contribution_c) 0.22 0.56 -0.90 0.98 1.00
## Bulk_ESS Tail_ESS
## sd(Intercept) 2869 5843
## sd(self_contribution_c) 4163 6858
## cor(Intercept,self_contribution_c) 6576 8996
##
## Population-Level Effects:
## Estimate Est.Error l-95% CI u-95% CI Rhat
## Intercept 1.02 0.10 0.83 1.21 1.00
## phi_Intercept 4.36 0.22 3.92 4.78 1.01
## subclusterEM -0.05 0.08 -0.21 0.11 1.00
## subclusterPS -0.05 0.10 -0.24 0.14 1.00
## subclusterSS -0.05 0.08 -0.22 0.10 1.00
## self_contribution_c 0.01 0.00 0.00 0.02 1.00
## difficulty_c -0.00 0.00 -0.01 -0.00 1.00
## subclusterEM:self_contribution_c -0.00 0.00 -0.01 0.01 1.00
## subclusterPS:self_contribution_c -0.01 0.01 -0.02 0.00 1.00
## subclusterSS:self_contribution_c -0.00 0.00 -0.01 0.01 1.00
## Bulk_ESS Tail_ESS
## Intercept 3447 6424
## phi_Intercept 805 1511
## subclusterEM 7408 9170
## subclusterPS 6067 8135
## subclusterSS 8400 8531
## self_contribution_c 6915 9556
## difficulty_c 7781 11003
## subclusterEM:self_contribution_c 6990 9443
## subclusterPS:self_contribution_c 6790 9282
## subclusterSS:self_contribution_c 8179 9742
##
## Draws were sampled using sampling(NUTS). For each parameter, Bulk_ESS
## and Tail_ESS are effective sample size measures, and Rhat is the potential
## scale reduction factor on split chains (at convergence, Rhat = 1).Perform hypothesis tests on the fixed effects coefficient:
hypothesis(dist_subset_self_mdl,
'difficulty_c < 0')## Hypothesis Tests for class b:
## Hypothesis Estimate Est.Error CI.Lower CI.Upper Evid.Ratio Post.Prob
## 1 (difficulty_c) < 0 0 0 -0.01 0 1332.33 1
## Star
## 1 *
## ---
## 'CI': 90%-CI for one-sided and 95%-CI for two-sided hypotheses.
## '*': For one-sided hypotheses, the posterior probability exceeds 95%;
## for two-sided hypotheses, the value tested against lies outside the 95%-CI.
## Posterior probabilities of point hypotheses assume equal prior probabilities.hypothesis(dist_subset_self_mdl,
'self_contribution_c > 0')## Hypothesis Tests for class b:
## Hypothesis Estimate Est.Error CI.Lower CI.Upper Evid.Ratio
## 1 (self_contributio... > 0 0.01 0 0.01 0.02 614.38
## Post.Prob Star
## 1 1 *
## ---
## 'CI': 90%-CI for one-sided and 95%-CI for two-sided hypotheses.
## '*': For one-sided hypotheses, the posterior probability exceeds 95%;
## for two-sided hypotheses, the value tested against lies outside the 95%-CI.
## Posterior probabilities of point hypotheses assume equal prior probabilities.hypothesis(dist_subset_self_mdl,
'subclusterEM:self_contribution_c < 0') # PSTQ is reference## Hypothesis Tests for class b:
## Hypothesis Estimate Est.Error CI.Lower CI.Upper Evid.Ratio
## 1 (subclusterEM:sel... < 0 0 0 -0.01 0 2.04
## Post.Prob Star
## 1 0.67
## ---
## 'CI': 90%-CI for one-sided and 95%-CI for two-sided hypotheses.
## '*': For one-sided hypotheses, the posterior probability exceeds 95%;
## for two-sided hypotheses, the value tested against lies outside the 95%-CI.
## Posterior probabilities of point hypotheses assume equal prior probabilities.hypothesis(dist_subset_self_mdl,
'subclusterPS:self_contribution_c < 0') # PSTQ is reference## Hypothesis Tests for class b:
## Hypothesis Estimate Est.Error CI.Lower CI.Upper Evid.Ratio
## 1 (subclusterPS:sel... < 0 -0.01 0.01 -0.01 0 5.67
## Post.Prob Star
## 1 0.85
## ---
## 'CI': 90%-CI for one-sided and 95%-CI for two-sided hypotheses.
## '*': For one-sided hypotheses, the posterior probability exceeds 95%;
## for two-sided hypotheses, the value tested against lies outside the 95%-CI.
## Posterior probabilities of point hypotheses assume equal prior probabilities.hypothesis(dist_subset_self_mdl,
'subclusterSS:self_contribution_c < 0') # PSTQ is reference## Hypothesis Tests for class b:
## Hypothesis Estimate Est.Error CI.Lower CI.Upper Evid.Ratio
## 1 (subclusterSS:sel... < 0 0 0 -0.01 0 2.57
## Post.Prob Star
## 1 0.72
## ---
## 'CI': 90%-CI for one-sided and 95%-CI for two-sided hypotheses.
## '*': For one-sided hypotheses, the posterior probability exceeds 95%;
## for two-sided hypotheses, the value tested against lies outside the 95%-CI.
## Posterior probabilities of point hypotheses assume equal prior probabilities.This completes this analysis.